Yes, a betta fish can live without a filter. In the wild, bettas can even live in murky pools of water for a period of time. However, without a filter, you’ll need to change the tank water at least twice a week. This will prevent harmful microorganisms and toxic wastes from building up and poisoning your betta.
If changing the water twice a week too much work, then you should get a filter, but be cautious when choosing a filter. If the filter current is too strong, your betta might get sick, stressed, or even die. Try using sponge filters or a filter with a weaker output. For example, if you have a 5-gallon tank, use a 1-3 gallon filter.