I was wondering, is there some function in the game settings which would allow me to make the player character's magicka increase by one tenth of their intellect when they level up? Or a similar effect?

There's no game setting that affects the magicka increase every level. But you could increase fPCBaseMagickaMult each level to change the base magicka value. This is then multiplied by the Intelligence x2 and increased by the various race and birthsign modifiers.