Țicleanu began his youth career with Metallurgistul Sadu in 1974. He was quickly spotted there by manager Constantin Oţet who brought him to Universitatea Craiova in 1976. He made his professional debut at age 17 with Craiova during the 1976–77 season. Țicleanu spent nine seasons at the club, and won the league title twice, in 1980 and 1981 also reaching the semi-finals of the UEFA Cup in 1983.
In the 1985–86 season, he joined Sportul Studențesc of Bucharest, helping them to a second place finish in the Divizia A the club's highest ranking ever. He remained at the club four seasons, before joining Cypriot side Olympiakos Nicosia, from where he retired in 1991.