No feats really meet this need, and those that may come close aren't very attractive
A feat that grants a creature that can't cast spells a warlock-style ersatz eldritch blast that scales with the creature's Hit Dice isn't, so far as I can tell, a thing. I mean, below are a few feats that may be interesting, but they're pretty much it. They're also kind of bad, possess intense prerequisites, or both.
Feats that grant a mundane creature a ranged attack that scales with level but has limited uses per day
The question asks for unlimited-use abilities, and these aren't those, but there are so few options available that including these seemed natural, for comparison if nothing else. Skip to the next section if these aren't of interest.
- The general feat Ki Barrage (Dragon #306 54–5) has absurd prerequisites: a Dexterity score of 16 (yes, that's both accurate and nonstandard), a Wisdom score of 19, and the feats Improved Unarmed Strike (Player's Handbook 96), Precise Shot (98), Point Blank Shot (ibid.), and Stunning Fist (101) and this last feat itself also has a prerequisite of a base attack bonus of +8 if not acquired as, for instance, a monk bonus feat. Anyway, the feat allows the creature to make normal ranged attacks (i.e. it can make its iterative attacks when it takes the full attack action) that possess a 30 ft. range increment and deal the creature's unarmed strike damage except the damage is force damage; each attack expends a use of the Stunning Fist feat. Even a nonmonk's unarmed strike damage can scale with character level—albeit not very well—via the feat Superior Unarmed Strike (Tome of Battle 33). Don't marry the feat based on my description here: A raft of other restrictions apply; read the feat yourself first. It's terrible.
- This fine answer already mentions the domain feat Magic Devotion (Complete Champion 61) that has no prerequisites and allows the creature 1/day to take a standard action to use a supernatural ability to make a ranged touch attack against a target within 30 ft. +5 ft./character level that, if successful, deals 1d6 points of damage per 2 character levels. The feat can be used again by expending 2 turn undead attempts or by taking the feat multiple times. As a DM, I've found the feat Magic Devotion occasionally attractive for monsters that otherwise lack a ranged attack (e.g. a mildly optimized advanced (7 HD) wight Clr 1 can typically employ the feat Magic Devotion 4/day and is about CR 4 if the Monster Manual is to be believed and if that matters).
- The general feat that's also a fighter bonus feat Ring the Golden Bell (Dragon Compendium Volume 1 105) possesses prerequisites that are still absurd, but not quite as absurd as the Ki Barrage feat: A Wisdom score of 13, a base attack bonus of +5, and the feats Improved Unarmed Strike, Stunning Fist, and Weapon Focus (unarmed strike) (PH 102). This investment gives the creature the ability to make an unarmed strike as a ranged attack with a range of up to 5 ft. +5 ft. × the creature's Wisdom bonus. The creature can make such an attack but 1/day + a number of times per day equal to the creature's Wisdom bonus. Again, the feat Superior Unarmed Strike sees a creature's unarmed strike damage scale with character level.
Feats that grant a mundane creature a ranged attack that scales with level and has no use limit
These are actually what the question asks for. Okay, not really. They approach what the question asks for.
- The martial arts style Northern Fist Mastery (Dragon #315 66) isn't a feat but I think it's close enough because it's gained automatically by a creature that possesses all of the following feats: Combat Expertise (PH 92), Falling Star Strike (Dragon #303 60), Freezing the Lifeblood (Complete Warrior 99), Improved Unarmed Strike, Pain Touch (CW 103), Stunning Fist, and Unbalancing Strike (Oriental Adventures 66). (So you know, those feats, in turn, mandate a Wisdom score of 17 and a base attack bonus of +10.) In other words, there's no reason for a creature to take all those feats except to get this style, and for all those feats the creature gains the ability to take a full-round action to make one ranged attack against a target that's within 5 ft. per 5 character levels. (That's not a typo—its maximum range is 10 ft. at levels 10–14, for example.) If successful, the attack deals the creature's unarmed strike damage. Once more, the feat Superior Unarmed Strike sees a creature's unarmed strike damage scale with character level. Really, just don't do this.
- The monstrous feat Spit Venom (Serpent Kingdoms 147) has as a prerequisite a poison bite attack. The feat allows a creature to make a ranged touch attack at a target within 30 ft. that, if successful, delivers the target's poison as if it were a contact poison. In the same book is the yuan-ti graft poison fangs (154) (8,000 gp; graft) that grants a poison bite that, if successful, deals 1d6 points of Constitution ability damage as its primary damage and secondary damage. The saving throw DC against this poison scales with character level (DC = 10 + ½ the creature's Hit Dice + the creature's Constitution modifier). (Other methods of gaining a poisonous bite are beyond this question's scope, but if this option's entertained, this answer may also be of interest.) While Serpent Kingdoms is chock-a-block with broken material (e.g. the manyfang dagger (152 and here), the sarrukh (80–1 and here and everywhere), venomfire (158 and here)), this reader doesn't consider among that broken material the feat Spit Venom (see below).
- The general feat Thunderclap (Savage Species 40) has as its prerequisite the feats Improved Unarmed Strike (Player's Handbook 96) and Power Attack (98) and a Strength score of 30. Yes, 30. Such a creature can at will take a standard action to create a 5-ft.-per-Hit-Die cone (read that again) that requires those caught within to make a Fortitude saving throw (DC = 10 + ½ the creature's Hit Dice + the creature's Constitution modifier). Success means the victim is unaffected. Failure means that for the encounter the victim is deafened (and 20% spell failure is a debuff not to be scoffed at). Failure by 5 or more also means that the victim is rendered prone (also no scoffing—see here). Again, my strong high-HD monsters have used this feat to good effect, but it also works for Hulk-level-strength PCs. (To be clear, though, this effect deals no actual damage.)
(This list excludes feats like Earthquake Stomp (Secrets of Xen'drik 134), Mighty Roar (Savage Species 37), and Shockwave (Draconomicon 73) that have effects that aren't really per se ranged. (The feat Thunderclap is included even though it's a cone because the cone is usually so big that it might as well be ranged.) Also excluded are feats like Fling Ally (Races of Stone 139–40) et al. and Rock Hurling (143) et al. that require ammunition.)
Obviously, the "winners" in the list above are the feats Spit Venom and Thunderclap, and, given the latter's prerequisites, the former's probably the only viable one. However, way too many creatures are immune to poison. (For example, creatures immune to poison include any creature that possesses the type construct, elemental, ooze, plant, or undead plus any outsider that possesses the subtype baatezu or tanar'ri.) At high levels, a PC will be lucky to fight a foe that's vulnerable to poison… then that PC must be even luckier to have that foe fail the initial Fortitude saving throw against the PC's poison. Good luck.
Were I asked, my recommendation for a multiclass character that's looking for a scaling ranged attack would be to have the character invest skill ranks—and possibly also feats—into the the skill Use Magic Device. The amount of gp a PC earns from adventuring scales by level so the magic items a PC buys do, too. Just buying a better ranged attack is way easier than trying to get feats to do what magic items should be doing for the PC.