Announcing the signing, Wrexham said: "Foster, 23, will provide short-term cover for the goalkeeping department, while Arthur Okonkwo (wrist) and Callum Burton (thigh) recover from their respective injuries, and help to share the training workload.
"He has been registered to play, and is available for selection if required.
"Foster has been training with the Red Dragons for several weeks, alongside Mark Howard, Liam Hall and Callum Burton prior to his injury".