The former Scotland Under-20 internationalist has been registered for this weekend’s Challenge Cup match against London Irish, with Stuart McInally dropping out due to injury.
McInally suffered a knock to the neck area during Saturday’s win over Cardiff and was taken off at half-time.
Edinburgh said McInally’s withdrawal from the European tie was a “precautionary measure” and he is expected to return to full training next week.
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Renwick, 24, was part of the Southern Knights side which reached the final of the FOSROC Super6 in October.
He came through the youth system at Hawick and played senior rugby for the Greens and more recently Watsonians.
He won Scotland age grade caps at U18, U19 and U20 level and is a Scottish Club International.
Dave Cherry replaced McInally against Cardiff and is expected to start against London Irish in Brentford on Saturday. Edinburgh also have Adam McBurney in reserve.