They're not a very active fish, they spend a lot of their time moving slow and calm or resting on the floor or broad leafed plants.
Chances are though, that he's cold. Get his temp up to around 78-80, this is the best range for them, they are a tropical fish after all. Betta can TOLERATE being cold, but they don't WANT to be cold, and just like us, being too cold for too long can lead tot a whole host of health issues. Most pet stores will sell a small 14 dollar heating pad that should do the trick, it's slim and can be placed against a wall or under the gravel.
Best of Luck!