"A lot of tough decisions this spring," manager Mike Scioscia said, "but we're really comfortable that those guys are going to give us the depth we're going to need in our 'pen."
Parker, claimed off waivers from the Brewers in December, pitched his way into a roster spot this spring, posting a 0.73 ERA with 24 strikeouts through 12 1/3 innings.
"What he's done so far is very real," Scioscia said. "His ability to repeat pitches has been very impressive."
Parker ended exhibition play on a high note with each of his last 17 outs coming via strikeout, longer than any such streak in the regular season since 1974, per STATS LLC.