Rencher was a prep star at St. Raymond High School for Boys in the Bronx, New York, earning New York City MVP honors in his senior year. Rencher attended the University of Texas at Austin, being drawn to the high-paced tempo of play that coach Tom Penders employed. There he finished his career with 2,306 points (making him both the school's and Southwest Conference's all-time career scorer in men's basketball) and 440 assists. He was selected by the Washington Bullets in the 1995 NBA draft, but his draft rights were traded along with Rex Chapman to the Miami Heat, for the draft rights to Jeff Webster and Ed Stokes. He was traded midway through his rookie season (1995–96) with the Heat to the Phoenix Suns, in exchange for Tony Smith. Internationally, he played for Bnei Herzliya in Israel, Pallacanestro Cantù, Basket Rimini and Viola Reggio Calabria in Italy, KK Split in Croatia and Telekom Baskets Bonn and RheinEnergie Köln in Germany, amongst others.