Rentzias was selected with the 23rd overall pick by the Denver Nuggets, in the 1996 NBA draft, while still under contract with PAOK. Rentzias opted not to play in the NBA at that time. On 29 September 1997, Rentzias' player draft rights were traded by the Denver Nuggets, along with a future 2000 2nd-round draft pick (Hanno Möttölä was later selected), to the Atlanta Hawks, in exchange for Priest Lauderdale. On 26 June 2002, Rentzias was traded by the Atlanta Hawks, to the Philadelphia 76ers, in exchange for a future 2004 2nd-round draft pick (Royal Ivey was later selected), and a future 2006 2nd-round draft pick (Daniel Gibson was later selected).