(Battle Master) Fighters can make good Intelligence based characters
Disclaimer : this answer presents you with one option, but there are other (maybe better) possiblities. This option requires DM collaboration, as it's a non-standard way of playing.
Your goal is to play a character who focuses on Intelligence without being an actual spellcaster. A high Intelligence, when not used for spellcasting, gives better Investigation, History, Nature, Arcana and Religion checks (and better Intelligence saving throws, but these are rather rare). It also gives a better chance to remember details from previous sessions ("Memory" checks). Your goal is to have a more-than-roleplay-only purpose, so you probably want to make a use of these skills for combat-related purposes. In other words, you want a mechanical, non-magical advantage to having a high INT score.
So, of the 12 classes, we can eliminate those with spellcasting or other supernatural power : Bards, Clerics, Druids, Paladins, Rangers, Sorcerers, Warlocks and Wizards. We can also eliminate Barbarians, whose general playstyle is often considered "mindless", especially when they rage. Monks can be discarded as well, as they mainly focus on the Wisdom mental ability, which is not what you seek there. This leaves us with Fighters and Rogues. Another answer already focuses on Rogue archetypes that would fit your needs, so let's focus on Fighters here.
I am aware that Fighters in general don't have class features that use Intelligence per say. However, Fighters, unlike Barbarians, focus on tactics more than brute strength to win fights, and as explained below, a good Intelligence can give you better tactics, thus befitting the class's efficiency.
There are currently 7 Fighter Archetypes : Champion, Battle Master, Eldritch Knight, Purple Dragon Knight, Arcane Archer, Cavalier and Samurai. Eliminating Eldritch Knight and Arcane Archer because of their supernatural powers, that leaves us with 5 choices. This answer focuses on Battle Masters, which are, by definition, specialized in controlling the battlefield, and thus more fit to command, lead and make tactical decisions, all of which can benefit from a good Intelligence.
Below are ways for a (Battle Master) Fighter to benefit from good Intelligence checks in (preparation of a) battle :
History : Study the tactics of previous commanders in order to apply them in your own encounters. (the Art of War by Sun Tzu is a great example)
Nature : Study the geographical advantages of different terrain types in order to better position your troops and make better ambushes
Investigation : While in combat, analyze the situation to find weaknesses in the enemy's defenses in order to give better orders to your troops to exploit said weaknesses
Arcana : Know about the magical properties of creatures in order to better plan against them
Religion : Know the values of certain deities in order to better convince faithful NPCs to join you into battle; Get to exploit divine properties, such as holy water, to your advantage
There is also an optional rule for a DM to use a different ability bonus than the traditional one for the existing skill checks, when the situation may call for it. These skills can be instead used with Intelligence with clever roleplay and DM approval :
(INT) Intimidation : Explain to your enemy how he is tactically overpowered and should surrender before getting crushed in battle.
(INT) Persuasion/Deception : Using information about the target (possibly obtained by an Intelligence skill check like Investigation, History or Religion) to sway him in your favor in a clever, well-structured way
And more, up to your imagination !
By focusing on Intelligence, you will not do as much damage as other martial classes, but you will be able to place your party in advantageous scenarios where they will be more efficient thanks to you. You will probably want to take 1 level of Rogue, 3 levels of Bard and/or the Prodigy feat [Xanathar's Guide to Everything] to benefit from Expertise on one or more of these skills.
Synergy with (Battle Master) Fighter features
Some skill checks require a full action to use. With the Fighter's Action Surge, you can spend your regular action to Investigate something critical for your success on the battlefield, then spend the Surge action to act in response to the investigation's results.
The Protection Fighting style, for example, is the most useful when you are placed properly on the battlefield (beside an attacked ally). A previously successful intelligence check might have given you the perfect spot (ex: tunnel) to set up your troops.
The level 7 "Know your enemy" feature in particular combines very well with Investigation checks to get extra information on your enemies. Also, intelligence checks enable you to memorize information obtained in the past, so you can better retain enemy info you get by the "Know your enemy" feature.
Below are also some combat maneuvers that benefit from a good Intelligence :
Commander's Strike : your prior battlefield placement will be even more beneficial to your damage dealing teammates, as you will allow one of them to strike once more per turn with the possible Surprise you inflicted on your enemies thanks to your Intelligence-planned ambushes.
Maneuvering Strike : if an Intelligence check makes you see a breach in the enemy's defense, you will probably want to move your damage dealers towards the best spot to exploit it. This maneuver allows you to do exactly that.
Precision Attack : Many tactical possibilities here, especially if you have weapons who deal effects on a hit, like a net.
Pushing Attack : If you have cleverly prepared the battlefield with artificial or natural traps (Nature check?), this maneuver makes you benefit from it by moving the enemies in disastrous positions.
And more, up to your imagination !
Going further : Siege tactician
It may sometimes happen that combat won't happen in an empty field, but rather with defensive fortifications for one (or both) sides. History checks might give you info about ancient secret passages leading right behind the enemy's walls. Nature checks might let you know that the natural foundations of the enemy's castle are unstable and could be impared (ex: digging under). Investigation checks might help you understand the mechanism of complex siege weapons, or even build/repair said mechanism. All of these options pair nicely with Commander-like characters, and therefore can synergize well with (Battle Master) Fighters.
So, with all that said, you have a perfectly viable way to focus on Intelligence while playing a martial class like a Battle Master Fighter, even if, by default, Intelligence was not used in the class's features per say. Dungeons and Dragons is and should not be limited to what's written in the core features : if you want to go further and be a "martial nerd", this option is for you. I don't expect this answer to be the accepted one, but it can still be useful for the eventual reader.