He goes straight into the Imps' squad for Friday's match at Rotherham.
Prior to the signing Paul Musselwhite had been Lincoln's only keeper, with Joe Anyon loaned to Morecambe and Trevor Carson recalled by Sunderland.
Carson has since joined League One side Brentford on loan.
Parish is Lincoln's second signing of the day, after Portsmouth midfielder Tom Kilbey, 20, signed a loan deal until the end of the season prior to the loan transfer deadline which passed at 1700 GMT on Thursday.
Source: BBC Sport
Source: BBC Sport