That is too small. For Betta fish, you need 2.5 gallons MINIMUM. Which means that you will have to get a bigger tank. Well, what do you think you should put in the tank? Plants, gravel, filter, heater. Use water conditioner.
My goodness, y-e-s! To be healthy, bettas need 2-3 gallons minimum.Don't be stupid and think that they enjoy being in a vase or cup. That is supposed to be TEMPORARY housing for the fish. Also, bettas have a labyrinth lung that allows them to breath directly from the air. They need some empty "air space" to be healthy.
Bettas enjoy many crevices and vegetation. Put in a little cave like item and some specialized betta plants that are sold at Wal-Mart.