Born in Quilmes, Rodríguez began his career on Independiente, joining the club's youth categories in 2000, aged 10. On 10 February 2008, he made his first team debut, in a 0–1 loss against Lanús. On 15 March, he provided an assist for Germán Denis' goal in a 3–1 win against Gimnasia La Plata. On 5 April, he was handed his first start, in a 1–3 loss against Colón. On 30 August 2009, Rodríguez scored his first and second professional goals, against Atlético Tucumán.
On 20 July2012, Rodríguez signed a four-year contract with Brazilian Série A club Santos. On 11 August, he made his debut for Peixe, scoring the first goal in a 2–2 draw against Atlético-GO. On 31 July 2013, Rodríguez signed with Estudiantes de La Plata, in a season-long loan deal. He returned to Santos in the 2014 summer, but was sparingly used. On 19 February 2015, Rodríguez was loaned to Johor Darul Ta'zim until November.
On 20 July 2016, Rodríguez signed a two-year contract with Greek side AEK Athens, with an annual salary of €500,000. He made his official debut against Xanthi, providing his teammates with 2 assists and helping his team secure a comfortable 4–1 win. On 14 October 2016, AEK's winger was suspended with a three-match ban for his unprofessional behavior against Diogo Figueiras in a 3–0 away loss in the derby clash against Olympiakos. On 5 November 2016, he scored his first goal in a 2–2 home draw against Atromitos. On 10 December 2016, he scored in a 4–0 win against Levadiakos. On 13 April 2017 Patito scored the winning goal in a 2–1 Greek Cup semifinals first leg away win against champions Olympiacos. Despite the rumours from the beginning of 2017–18 season, it was reported Rodríguez would remain a member of AEK until the end of the season, when his current contract with the historic club expires. Eventually on 8 December 2017, he released from the club by mutual consent.
On 22 December 2017, Newcastle Jets announced signing Rodríguez as an injury replacement in the January transfer window, replacing their injured marquee Ronald Vargas. He scored on his debut for Newcastle Jets in a 2–0 win over rivals Central Coast Mariners. Following Vargas's recovery from injury and re-signing with Newcastle Jets, the club announced Rodríguez's release on 16 May 2018.
