Twardzik grew up in Middletown, Pennsylvania, and played collegiately at Old Dominion University, where he was a two-time All American and led the Monarchs to the 1971 NCAA Division II title game. He was drafted by the Trail Blazers in 1972, but elected to play for the Virginia Squires of the ABA. Twardzik played for the Squires for four seasons until the team (and the ABA) came to an end, folding just prior to the ABA-NBA merger in June 1976. After the ABA-NBA merger Twardzik signed with the Blazers as a free agent. He would be the starting point guard of the Blazers team which won the NBA title in 1977. He played for four seasons total in Portland, and retired at the end of the 1979–80 season because of injury. His jersey number (13) was retired by the team.