Catching an injured chicken

Hello everyone. I live in a neighborhood where chickens are constantly roaming the streets and houses. Yesterday I noticed a young hen who appears to have some eye infection as she is unable to open one eye and the other eye barley open. She is docile, but keeps bumping into objects/curbs. She is able to fly as well. I contacted a rescue who is willing to take her in, but I will have to catch her.

I have no experience in catching chickens and just don’t feel comfortable doing it. I’ve been trying all morning but I am stressing her out. I tried with a towel but it scared her and she flew away. Any other tips? I don’t have a animal cage and don’t have the means to get one either.

She’s walking around with one eye completely shut and the other a little open but it is visibly red. She is mobile, just bumping into objects.