Depends on the cichlid..

Some are big enough to eat it (oscars, angelfish, JDs), some will just slaughter it (Kenyi's, Bricardis, electric blues, yellow labs), and others might have a chance.. (little shell dwellers).

Edit..
Erm Ian? Angelfish aren't small. lol. They can get a good 10 inches high and long and easily fit a betta into their mouth.

Its not recommened but if the cichlid is small and not aggressive then go ahead.

What cichlids?

Smaller ones like Kribensis, Keyholes or even Angelfish.. yes they should be fine togther.

Bigger and/or more aggressive ones like Oscars or most African Lake species will just slaughter your betta, or in the case of the Oscar, swallow it whole.

Cichlids are a HUGE family of fish that range from shy little fish about 1" long to huge 2 ft long predators. So asking about cichlids in general is not much use, you need to work out what species you intend to mix.

Ian

smaller species may be okay while bigger ones will eat them.

me

i have female bettas in with rams and they are fine together.

I've found that most female bettas rather would be alone. I put one in my 55 gallon with 2 angelfish, a couple tetras and a dwarf gourami or two and she freaked out and wouldn't leave the corner. If I had an angelfish swimming at me, I'd do the same thing. She immediately got stress lines also. She's been in a 6 gallon by herself for about 5 months and seems to like that more. Stress lines have been gone for about 4 and a half months and she swims all over. Some females may be fine, but most that I've seen in community tanks tend to have stress lines. You can try it but don't be surprised if she gets eaten, tormented or shows signs of stress. If she's showing signs of stress, remove her as soon as possible.