Fischer attended Westside High School in Omaha and the University of Nebraska–Lincoln. Fischer joined the NFL as the 17th-round draft choice of St. Louis in the 1961 NFL Draft. He then signed with Washington as a free agent in 1968. He was a 1969 Pro Bowler. In 1972, the Redskins won the NFC championship game of the 1972-73 NFL playoffs against the Dallas Cowboys, when they limited Roger Staubach, their quarterback, to only 9 completions in 20 attempts for 98 passing yards and 3 allowed sacks, Fischer and Mike Bass, the other cornerback, being particularly successful in shutting down their wide receivers. But though the Redskin defense allowed only 69 net passing yards, it could not stop the Miami Dolphins's running game (184 rushing yards) in losing Super Bowl VII.
He finished his 17-year career with 56 interceptions, and ranks seventh all-time in Redskins career interceptions with 27 and fourth all-time with 412 career interception return yards. At the time of his retirement, Fischer had played in 213 NFL games, then a record for a cornerback. He was well known for his strong tackling skills despite his diminutive size. Some of Fischer's most memorable defensive match-ups occurred against Philadelphia Eagles receiver Harold Carmichael who stood eleven inches taller than Fischer. Fischer's mantra "get a leg up and you own him" is used today to motivate and teach smaller defensive backs how to defend taller wide receivers.
In the late 1980s, NFL Films named Fischer as the Redskins All-Time Neutralizer sponsored by Tums. After retiring from the Redskins, Fischer worked as a stockbroker and owned a successful real estate business.