The women, aged 69 and 71, were each targeted in separate attacks in the 200 block of South Anita Avenue.
Police say one woman was returning her trash bin to the backyard when the man struck. He tried to pull off her ring, but she screamed and got away.
The other woman was also targeted on trash day. Her finger was broken as the attacker stole her wedding ring.
Police say the man took off with an accomplice in an orange, two-door sports car.