The rat ran over to a dog walker who found her in Elsecar on Monday March 5 and he managed to pop her into a box before contacting the RSPCA.
She has been nicknamed Midge by RSPCA staff who are looking after her at a rescue centre in Chesterfield.
Insp John Gibson who collected the young pale grey pet said: "At this stage we do not know if she escaped or if she was dumped but I suspect it was the latter as she was in the middle of a field with no houses around to suggest she is a stray.
“Luckily the passerby spotted she was a domestic rat as she is so friendly and came running over to greet her.
“We are appealing for anyone with information on how this lovely rat came to be in the field to contact us on the inspectorate appeal line on 0300 123 8018."
If her owners don't come forward then she will eventually be rehomed.