He began the season with the Chiefs once again in 1992, where he had a 12–10 record with a 3.74 ERA in 25 starts, earning a call-up from the Toronto Blue Jays. Linton made his Blue Jays debut on August 3, 1992, where he pitched 3.2 innings out of the bullpen, allowing one run and striking out four as Toronto lost 7–1 to the Boston Red Sox at Fenway Park. He made his first major league start on August 13, as Linton pitched eight innings, allowing two runs and striking out four, as the Blue Jays defeated the Baltimore Orioles 4–2 at SkyDome to earn his first major league victory. Linton struggled after that game, allowing 19 earned runs in six innings over four appearances, and was sent back to the Chiefs at the end of August. Linton had a 1–3 record with an 8.62 ERA with Toronto.