No, not at all. A betta needs at least a 2.5 gallon (some will say a 5 gallon).
They are tropical fish and need a heater and a filter as well.
There is a commonly spread myth that bettas live in puddles in the wild, which has lead people to believe tiny tanks are okay for bettas. This is not true.
Wild type bettas life in shallow, long bodies of water. So even though it might not be deep they have miles and miles to swim.
I would suggest buying a:
• 5 gallon aquarium
• Heater suitable for 5 gallons
• Filter suitable for 5 gallons
• A live plant, or a very soft fake plant
• Some sort of hiding place for the betta
• API master test kit (for water parameters)
• Water conditioner
You can do a fish-in cycle with your betta, placing him in the new tank and letting the water cycle. Read a few articles on the nitrogen cycle.
The sad truth is that your betta can quickly get sick and die if kept in such a small, unfiltered tank.
even though fish may seem like an easy pet to keep their care is very complicated. Large Petstore (like Petco and Petsmart) workers are usually not very knowledgeable about the fish they carry.
for now fill up the tank you currently have to the very max, and preform 50% water changes a day until you can get the new tank.
I know it seems like a lot of work, but your betta will thank you.
If you are a beginner, I would recommend a 10 gallon actually since that means the tank will get fouled less quickly. I agree with AquaCaitlin. YOu should buy all those things and cycle the tank. For the tank setup, if you want it to be easier to maintain, I would get a 10 gallon with a really good filter, a heater(one that keeps the temperature stable at 78-82 degrees farenheit), water conditioner, and again, basically everything AquaCaitlin suggested. I would also get floating plants such as hornwort, java moss and giant duckweed. With a setup similar to this and a good feeding routine(for example feed 5 or 6 times a week. Don't overfeed) you can go as long as a month without water changes. Sorry if this has scared you, fish keeping can be fun and relatively easy as long as you do it correctly