I'm looking for a way to execute a charge as a move action. Movement without using a move action would work but is limited.
Not without also falling or jumping
The regional feat Battle Jump (Unapproachable East 42) grants the creature the ability to "execute a charge by simply dropping from a height of at least 5 feet above [its] opponent." The Dragon #327 Sage Advice column “Official Answers to Your Questions” says that
If you’re capable of making a high jump that brings you at least 5 feet above an enemy, you could employ the Battle Jump feat… without having to start at a higher location. Of course, that would require a Jump check result of at least 40 for a Medium opponent, so it’s out of reach of most characters. You’d also have to make the Jump check from adjacent to your foe, so it would provoke attacks of opportunity (since you’re moving upward out of a threatened square). All in all, it sounds like a pretty tricky maneuver, but cinematically very exciting indeed. (81)
This is reprinted almost verbatim in the D&D Frequently Asked Questions (72), with which some folks have issues.
As it's regional, the feat Battle Jump can only be taken by a taer from the Icerim Mountains, other creatures—including taers from other regions—having somehow lost or never discovered the complicated art of falling on their enemies.
Similarly but more controversially, the tactical feat Roof-jumper (Cityscape 62-3) via the tactical maneuver death from above allows a creature to "deliberately leap down to attack a foe beneath [it; the creature] must drop at least 20 feet [and] must roll to hit; this qualifies as a charge attack, with all relevant bonuses and penalties," but what, exactly, qualifies as a charge attack means is the subject of heated debate.
Also similar but less controversial yet far more painful to acquire is the feat Mantis Leap (Sword and Fist 7 and never reprinted therefore valid in 3.5e campaign—see Why a Revision? (DMG 4)) that allows the creature to "[d]esignate an opponent who is within the maximum distance [the creature] can reach with a successful Jump check [and has the creature m]ake a normal Jump check; if [the creature's] check is successful, [it] can make a normal charge attack against the opponent… as part of the same action" as the Jump skill check. Damage is also increased. This feat is perhaps the only reason to take seven levels of monk, which must be taken to meet one of the feat's prerequisites.
Note that these are typically high-powered strategies, suitable for campaigns in which a mundane warrior is struggling to maintain his relevance in a party of increasingly campaign-dominating clerics, psions, and wizards. For most campaigns, I recommend instead contenting oneself with a standard action charge via the boots of the battle charger (Magic Item Compendium 76) (2,000 gp; 2 lbs.). Activate the boots as a swift action, enter a rage, charge, and pounce. If doing it correctly, whatever's at the charge's end is probably still dead.
I am willing to state that this doesn’t exist anywhere in the game.
It’s impossible to prove a negative, but
If this existed, it would get mentioned in char-op discussions. I read a lot of those, and have never seen such a mention.
It would get mentioned because it would be phenomenally powerful, and out of keeping with the rest of the game.
A charge consists of movement, an attack, and some bonuses and penalties. Attacking as a move action is basically unheard of in the game, so that would be rather inconsistent. More importantly, since this would count as a charge, it would benefit from all kinds of other bonuses—most notably pounce. Getting to charge as a move action and tacking a free full-attack onto the end of it, and then still having a standard action to work with, would be, again, phenomenally powerful.
In terms of movement without move actions, have a Q&A on the subject.