SAN FRANCISCO — The Giants are down to three starting pitchers on their 25-man roster.

After rookie left-hander Conner Menez recorded just five outs in his third career start on Sunday, the Giants optioned the starter to Triple-A Sacramento. San Francisco did not promote any players to the 25-man roster Monday, but the club can add a pitcher or position player ahead of Tuesday’s game against the Oakland A’s.

Madison Bumgarner, Tyler Beede and Jeff Samardzija are the only active starting pitchers on the 40-man roster, but that will change this week when the Giants play in Arizona.

Dereck Rodríguez will likely return from Triple-A Sacramento to start one of the club’s games against the D’backs, but the Giants will need a fifth starter prior to Sunday, August 18, which is when rookie Shaun Anderson is eligible to return from the 10-day injured list. With Menez ineligible to come back from the minors for 10 days and Rodríguez in line to pitch Thursday, Friday or Saturday, it’s unclear how the Giants will fill the extra vacancy in their starting rotation.

The Giants are listing Bumgarner as the probable starter for Tuesday’s game against the A’s with Beede slated to throw on Wednesday. Samardzija’s turn in the rotation falls on Thursday, but the Giants may opt to give him an additional day of rest between starts after the veteran right-hander logged eight innings in his last outing.

Manager Bruce Bochy may opt to have his bullpen cover all the innings for one of the team’s games in Arizona, but the club also has the choice of promoting top pitching prospect Logan Webb from Triple-A Sacramento. Outside of Webb, there are no other starters on the 40-man roster and no obvious candidates to be added until Johnny Cueto returns from a rehab assignment in September.

Webb was recently promoted from Double-A Richmond to Triple-A Sacramento after posting a 2.18 ERA in eight games this season. Webb was suspended for 80 games due to a positive test for a performance-enhancing drug, but is still highly regarded by the organization and considered the Giants’ highest-rated pitching prospect by MLB.com.

The Giants announced Monday that they have claimed right-handed reliever Burch Smith off waivers from the Milwaukee Brewers. To clear a 40-man roster spot for Smith, who will report to Triple-A, the Giants designated recently acquired pitcher Ryan Dull for assignment.

Dull was claimed off waivers last week from the Oakland A’s and allowed two runs in three innings at Triple-A Sacramento.