Darnold took part in positional drills, multiple media outlets reported. Last week, the 21-year-old showed up at practice in pads and a helmet, but did not participate.
The 39-year-old McCown sustained a thumb injury during Sunday's 27-13 setback to the New England Patriots. He has completed 43 of 79 passes for 411 yards with one touchdown and three interceptions this season.
McCown was in the midst of a career-best season in 2017 before suffering a fractured hand in December. He threw for 2,926 yards with 18 touchdowns and nine interceptions.
The No. 3 overall pick in this year's NFL Draft out of USC, Darnold has struggled in his rookie season, completing only 55 percent of his passes for 214.9 yards per game with an NFL-high 14 interceptions to 11 touchdowns. His 68.3 passer rating is the worst among starting quarterbacks in the NFL.
Darnold had his worst game in the 13-6 loss at Miami on Nov. 4, throwing a season-worst four interceptions while finishing 21 of 39 for 229 yards.