Can a cat get roundworms from another cat?

Yes it can. Not only that, but cats can transmit roundworms to people as well, and the cycle keeps going as people transmit them to other people. When cats digs in ground that has been contaminated by faeces from a cat that has roundworms, this can transfer the worms to the other cat. When people walk on the ground in bare feet and then touch their feet, or dig in the ground and then touch their faces with dirty hands, this is how roundworms can be transferred.

There is a related link that explains about how the roundworm cycle works.