But fellow loan forward Maheta Molango is being released back to Brighton after a month at the Racecourse.
The Dragons' problems up front are easing, with Lee McEvilly and Juan Ugarte close to full fitness and Chris Llewellyn back from suspension.
Club captain Neil Roberts remains sidelined with an ankle injury, but should be back in action soon.
Sunderland teenager Smith was at Leeds United's youth academy before switching to the Stadium of Light in January this year.
The Scot has yet to make a first team appearance for the Black Cats.
"Both Smith and Molango have come here and done well for us," Wrexham manager Denis Smith told the club website.
BBC