Well, usually they need some getting used to the new surroundings before they start eating well. I would give him a few days on that.
That does look like an awfully small tank though. I would recommend upgrading to at least 2-2.5 gallons so you can properly heat the tank (a hydor mini heater would be perfect). Plus, he will be MUCH happier in a more appropriately sized tank. The rule of thumb is 1 gallon per max. inch for the fish. Bettas get up to 2.5 inches.
After the upgrade, find a couple of nice plants that won't tear his fins and a little hiding cave or something along those lines. He will be set and you'll have a happy little Betta!
Oh and of course welcome to the forum!