Jeff Burroughs trade in December of 1976. When he arrived in Arlington, Roger was regarded as a very good swingman who was on the cusp of being a great starting pitcher. He just needed to develop his endurance a little.
Unfortunately for Moret, he spent the first part of the 1977 season on the disabled list following surgery to correct a circulatory problem in his left arm. He didn't return to action until June 28, 1977. In the remaining part of the season Rogelio put up some decent, but not outstanding, numbers. In 18 appearances he pitched 72.1 innings and posted a 3.73 ERA and an 1.705 WHIP. Not too bad for a guy coming off surgery after missing over half the season.
Texas had high hopes for Roger headed into 1978. His arm recovered and strengthened, it was hoped he would regain his 1975 form. Coming out of Spring Training, Moret was once again slotted as the swingman on the staff. On April 12, 1978 Rogelio got the nod to start against Detroit. Prior to the game he was found standing in front of his locker holding a shower shoe in an outstretched hand. He did not respond to anyone. 90 minutes later he was transported to a psychiatric hospital, still in a catatonic state. He stayed in the hospital for nearly a month. After release Roger attempted a comeback but couldn't defeat the demons within. On June 16, 1978 he went back on the disabled list for psychiatric problems and spent the rest of the season there.
While active in 1978, Moret appeared in seven games for Texas. He started two of those games. Over the 14.2 innings he pitched, Rogelio's ERA totaled to 4.91 and his WHIP to 1.705. He ended the season with a 0-1 record and one save.
The Rangers held on to Moret until Spring Training 1979 when it became obvious he would not be back. They released him on March 26, 1979. The Cleveland Indians signed him in January of 1980 but released him in March of the same year. He played in Mexico in 1980 and 1981 but never again took the mound in a Major League game.