Frandsen, 28, has played parts of five seasons with the Giants and Angels. He hit .250 in 2010 with the Angels over 160 at-bats, playing third base, first base, second base and the outfield.
Frandsen, who can also play shortstop, is a.243 hitter in 568 career Major League at-bats.
Frandsen, a right-handed hitter, had his best season with the Giants in 2007, hitting .269 in 109 games with five home runs and 31 RBIs.
According to ESPN, Frandsen will make $575,000 if he makes the Padres' Opening Day roster.
Quiroz, 29, has played parts of the last seven seasons in the Major Leagues with the Blue Jays, Mariners, Rangers and Orioles. Quiroz is a career .208 hitter in 255 at-bats.
Last month, the Padres completed a trade with the Mariners for catcher Rob Johnson. Johnson and Quiroz are expected to compete for the backup job behind Nick Hundley.
Hoyer said the Padres would still like to add a reliever and possibly a left-handed bat for the bench.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.