Vonk played as centre back and began his career in 1986 with AZ '67 for whom he played 111 times and scored 8 goals. He transferred to SVV Dordrecht in 1991 and played 51 times for the team scoring 1 goal. Then in 1992 he transferred to Manchester City F.C. where he enjoyed three successful seasons playing a total of 91 league games for the club, scoring 4 times. He had been brought in by then City manager Peter Reid costing £500,000. He formed a successful partnership with Keith Curle in the centre of the City defence. In 1995 he criticised then City manager Brian Horton in the News of the World which earned him a suspension and being fined 2 weeks wages.
Subsequent City manager Alan Ball sold the player to Oldham Athletic for £350,000, where he played 5 times and scored 1 goal. He was then transferred to Sheffield United where he played until 1998. He played 37 times for the Blades scoring twice. His time with the club was hampered by injuries. In 1998 he returned to the Netherlands and began playing for MVV Maastricht. His injuries continued however and he was released by the club when they were relegated.
In April 2011 Vonk agreed to return at Sparta as head coach for the 2011–12 season under supervision of newly appointed technical director Wiljan Vloet, who accepted to return at the Rotterdam club after two seasons as trainer of NEC Nijmegen.He was fired after one season. In July 2014, he started working for Telstar.