Bleier played college football at the University of Notre Dame in Notre Dame, Indiana, and graduated in 1968 with a degree in business management. During his junior season in 1966, the Fighting Irish won the national championship and he was a team captain as a senior in 1967. He was selected in the 16th round of the 1968 NFL/AFL Draft by the Pittsburgh Steelers, 417th overall.

 He played his first game on September 22nd against the LA Rams. He returned 3 kicks for 68 total yards. Rocky played a total of 10 games that season mainly as a kick returner, but also saw some time in the backfield. 

After his rookie season with the Steelers, Bleier was drafted into the U.S. Army on December 4, 1968, during the Vietnam War. He volunteered for duty in South Vietnam and shipped out for Vietnam in May 1969.

On August 20, while on patrol in Hiep Duc, Bleier was wounded in the left thigh by an enemy rifle bullet when his platoon was ambushed in a rice paddy. While he was down, an enemy grenade landed nearby after bouncing off a fellow soldier, he tried to leap over it and it exploded, sending shrapnel into his lower right leg. His right foot was severely damaged in the blast as well. He was later awarded the Bronze Star and Purple Heart.

While he was recovering in a hospital in Tokyo, doctors told him he should not expect to ever play football again. Soon after, he received a postcard from Steelers owner Art Rooney which simply read "Rock - the team's not doing well. We need you. Art Rooney". Bleier later said, "When you have somebody take the time and interest to send you a postcard, something that they didn't have to do, you have a special place for those kinds of people". After several surgeries, he was discharged from the Army in July 1970, and began informal workouts with Steeler teammates.

Bleier rejoined the Steelers in camp in 1970. Upon his return, he couldn't walk without being in pain, and weighed only 180 pounds (82 kg). He was put on injured reserve for the season, but returned in 1971 and played on special teams. He spent several seasons trying to get increased playing time, and was waived on two occasions. But Bleier never gave up, and said that he worked hard so that "some time in the future you didn't have to ask yourself 'what if?'". An offseason training regimen brought Bleier back to 212 lb (96 kg) in the summer of 1974, and he earned a spot in the Steelers' starting lineup.

In addition to being a great lead blocker, Bleier was the second of the Steelers' rushing weapons (Franco Harris was the primary back), but was effective nonetheless at both blocking and rushing. In 1976, both Harris and Bleier rushed for over 1,000 yards, making this the second NFL team to accomplish this feat, after Mercury Morris and Larry Csonka of the 1972 Miami Dolphins.

Bleier played in the first four Steeler Super Bowl victories, and caught the touchdown pass from Terry Bradshaw that gave Pittsburgh a lead it would never relinquish in Super Bowl XIII. He also recovered Dallas's onside kick in the closing seconds, sealing the Steelers' victory.

Bleier retired after the 1980 season, with 3,865 rushing yards, 136 receptions for 1,294 yards, and 25 touchdowns. At the time of his retirement, he was the Steelers' fourth all-time leading rusher.