Heaney, who threw a team-high 180 innings last season, missed the past two months with inflammation in his throwing elbow. He is 1-3 with a 6.57 ERA in seven career meetings with the Rangers.
He made a rehab start with Triple-A Salt Lake on Monday night and struck out 10 in 4 1/3 scoreless innings.
Heaney, who underwent Tommy John surgery in 2016, missed the first two weeks of last season with similar elbow soreness.
"We don't want any more issues with the arm," Angels manager Brad Ausmus said.
To make room for Heaney on the 25-man roster, the Angels put veteran right-hander Matt Harvey on the 10-day injured list with an upper-back strain.
Heaney will be opposed by Ariel Jurado (1-2, 2.08 ERA), who will be making his second start to go along with nine relief appearances for the Rangers this season.
Jurado made his only other start on May 18 against the visiting St. Louis Cardinals and went 4 1/3 innings, allowing four runs (two earned) and five hits in the 8-2 loss.
Jurado is 0-0 with a 5.40 ERA in two career meetings (one start) against the Angels.
Texas manager Chris Woodward told reporters that he's giving Jurado the start so he can break up Mike Minor and Lance Lynn in the rotation. Minor threw Saturday night and did not get the decision in the 3-2 loss, limiting the Angels to one run and five hits in six innings.
Lynn is scheduled to start the series opener at the Seattle Mariners on Monday.
"I've been waiting for an opportunity to kind of break them up for a number of reasons," Woodward said. "It's nice to have them back-to-back, but it also makes it harder to navigate through the other three days."
Jurado will face an Angels lineup that's looking for some of its better hitters to break out of mini slumps.
The Angels have been getting some solid performances from other parts of their lineup, however.
Kole Calhoun went 3-for-3 on Saturday night with an RBI double and solo home run. His double in the ninth inning tied the score at 2-2 and he scored the game-winner on a single by rookie Jared Walsh for his first major league RBI.
Since missing two games while on paternity leave at the end of the last road trip, Calhoun said he has been working on his mechanics with the Los Angeles hitting coaches.
"It's been hit or miss so I was able to dial some stuff in with the hitting coaches down there and it paid off," he said.
Angels infielder Luis Rengifo also had two hits on Saturday night and scored the tying run from first on Calhoun's double, running through a stop sign at third base.
The Angels acquired Rengifo from the Minnesota Twins during spring training in exchange for power-hitting first baseman C.J. Cron.
"We said all along, we really like this guy," Ausmus said of Rengifo. "He's short on experience, but we like the talent level and the ability. That speed is one of them."
--Field Level Media