Staiger was drafted out of high school by the Los Angeles Dodgers in the 15th round of the June 1969 amateur draft. He declined to sign with the Dodgers and instead attended Bacone College in Oklahoma. In the January 1970 amateur draft, he was selected in the 1st round by the New York Mets and signed with the Mets.
Staiger began his professional career with the Mets' class-A minor league team in Visalia in 1970. That season he played 76 games, with a batting average of .239, 7 home runs and 34 runs batted in.
In 1971 he played a second season at Visalia. That season he played 139 games, and his batting average improved to .282. He also improved to 19 home runs and 83 runs batted in. This earned him a promotion to the Mets' class-AA team, the Memphis Blues in 1972.
At Memphis in 1972, Staiger played in 81 games. He once again had a batting average of .282. But with only 3 home runs, his slugging percentage was just .379 and he registered an on-base percentage of .306.
For the 1973 season, Staiger was promoted to the Mets' class-AAA team, the Tidewater Tides. In 136 games, Staiger had a batting average of .249, a slugging percentage of .339 and an on-base percentage of .302. Although the Mets had several injuries to their infielders on the Major League team, Staiger was not called up to the majors during the season although several other Tidewater infielders — Brian Ostrosser and Lute Barnes — did receive time in the majors that season.
Staiger returned to Tidewater in 1974. Again he played in 136 games, and he improved his batting average to .272, his slugging percentage to .343 and his on-base percentage to .343. Again, he was not called up to the Mets major league team that season.
Staiger played for Tidewater a third consecutive season in 1975. In 137 games he improved his batting average and slugging percentage again to .282 and .418, respectively. This earned Staiger a promotion to the Mets major league team that September.
Staiger made his major league debut for the New York Mets on September 12, 1975. He played third base for the Mets that day against the St. Louis Cardinals. The following day, Staiger got his first Major League hit, a double, also against the Cardinals. In total, Staiger played in 13 games for the Mets in 1975, getting 3 hits in 19 at bats for a batting average of .158.
Staiger played the entire 1976 season with the Mets. Although he split time as the Mets third baseman with Wayne Garrett, he played the majority of the game at third base for the Mets that season, 93. In a total of 95 games in 1976, including one game in which he played shortstop, Staiger batted .220 with 2 home runs. His slugging percentage was .273 and his on-base percentage was .278.
In 1977, Staiger started the season with the Mets but was demoted to Tidewater in mid-season. He only returned to the Mets in September that season. In 40 games with the Mets that season he batted .252 with 2 home runs. In 73 games with Tidewater he batted .287 with 15 home runs.
After the 1977 season, Staiger was traded by the Mets to their cross-town rivals, the New York Yankees in exchange for Sergio Ferrer. Staiger played the entire 1978 season with the Yankees class-AAA team, the Tacoma Yankees. He batted .283 with 19 home runs in 118 games. The following season he again played with the Yankees AAA affiliate, this time the Columbus Clippers. He played in 104 games, with a batting average of .260 and 9 home runs. During the 1979 season he was briefly recalled to the Yankees major league team. He played 4 games for the Yankees, getting 3 hits in 11 at-bats.
In 1980 Staiger played once again for the Columbus Clippers. After batting .234 in 90 games, he ended his professional baseball career.