Walker will serve as an opener in Wednesday's game against the Mets, Alex Pavlovic of NBC Sports Bay Area reports.
Walker (2-2) struck out two in a perfect inning to earn the win Saturday over the Diamondbacks.
Walker (1-0) struck out two in a perfect inning to earn the win Sunday over the Padres.
Walker has allowed a hit and hit one batsman over two scoreless innings in Cactus League play.
Walker (4-3) allowed three runs on two hits and three walks while striking out two over two-thirds of an inning to take the loss in Game 1 of Saturday's doubleheader versus the Rockies.
Walker will serve as the Giants' opening pitcher for Tuesday's game against the Cubs at Wrigley Field.
San Francisco activated Walker from the paternity list Tuesday.
The Giants placed Walker on the paternity list Saturday, Evan Webeck of The San Jose Mercury News reports.
Walker struck out four over two scoreless frames while serving as the Giants' opening pitcher in Monday's 10-2 loss to the Rays. He worked around two hits and one walk in the 39-pitch outing.
Walker will serve as the opener for Monday's game against the Rays, Susan Slusser of the San Francisco Chronicle reports.