In 2000, Rodrigo entered the academy of Juventus and his junior career started off. He spent four years playing for the club's youth teams. In 2005, he was noticed by Avaí. Brito passed the preliminary tests and was drafted into the youth department of his new club. In 2006, Rodrigo signed a pro contract with Avaí for a period of two years. He didn't become the team's starter, making occasional appearances as a sub. In total, he appeared 31 times for the Brazilian squad. In the summer 2008, the footballer moved to Portugal to perform for Gil Vicente. He fitted the team perfectly, scoring 12 goals in 86 matches as a starter. In the summer 2011, Galo signed for Braga, but didn't get much playing time, so he was sent to his previous club – Gil Vicente. In 2012, he was sent on loan at Académica de Coimbra and later on to the Greek Super League side Panetolikos. In the summer of 2014, he played for Paços de Ferreira as a right back and right midfielder.
In March 2015, "AEK have not contacted my agent", the Pacos Fereira defender said. "My contract in the summer and I can talk with other clubs, but we have not discussed with AEK or any other team. The things will be different this year. Of course I am interested in playing for a great team, like AEK. I know they went through a crisis, but that doesn't mean anything. They will return to the Super League and it would be an honor for me to be part of the team". In May 2015 Rodrigo signed a two-year contract with the Greek club AEK. On 22 August 2015 he made his debut and scored his first goal for the club in a 3–0 home win against Platanias. On 25 October 2017 he opened the score in an easy 4–0 home win against Kerkyra for the Greek Cup. On 13 January 2017, AEK rewarded the Brazilian for his solid performances by extending his contract until the summer of 2019. On 20 December 2017 he scored against his old club, Panetolikos, in a 4–0 away win for the first leg of the round of 16 of the Greek Cup. On 1 April 2018, Rodrigo Galo with a simple low finish after an assist from Niklas Hult propelled Champions-elect AEK to a deserved 3–0 Athens derby win over 10-man Panathinaikos as Manolo Jiménez’s team inched closer to a first SuperLeague title in 24 years. On 8 August 2018, the administration of the team rejected an offer in the region of €500,000 from Süper Lig side Ankaragücü. On 14 August 2018, he opened the score after Niklas Hult’s low cross in a 2–1 home win game against Celtic for UEFA Champions League Third qualifying round, 2nd leg. On 29 September 2018, he scored with a beautiful free-kick in a 3–0 away win against OFI. On 12 October 2018, he scored with another stunning free-kick, sealing a 2–1 home win against Lamia for the Greek Cup. Since joining AEK in 2015, Brazilian right-back Rodrigo Galo has been a vital cog of the machine with his speed on the flank, but he will leave Athens on summer 2019 with his contract having reached its completion. In his four years with AEK, Galo only scored a grand total of eight goals, but nearly all of them were absolutely crucial. “I have been very happy during these four years, and we experienced amazing moments winning the Greek Cup, qualifying for the group stages of the UEFA Champions League and UEFA Europa League and claiming the national championship after a long hiatus,” said Galo after his AEK departure became public.
