Rodrigues joined Eredivisie club ADO Den Haag from amateur FC Boshuizen on 16 May 2012, signing a 1+1 years contract. In July, he was loaned out to Eerste Divisie club Dordrecht. Rodrigues made his league debut in a 1–1 away draw against Emmen on 10 August, playing the full 90 minutes.

On 11 February 2013, Rodrigues signed a two-and-a-half-year contract with Bulgarian club Levski Sofia. He made his debut away at Chernomorets Burgas in a 2–0 win on 3 March. On 13 March, he scored his first goal for Levski in the 22nd minute of a Bulgarian Cup quarter-final first leg tie against Litex Lovech. On 20 April, in a 2–1 away victory over Litex, Rodrigues netted his first league goal and assisted Hristo Yovov.

On 21 July 2013, Rodrigues opened the scoring in Levski’s first match of the 2013–14 A PFG season against Botev Plovdiv, but was subsequently sent off after an altercation with Veselin Minev.

Rodrigues received his first international call-up in August 2013 to play friendly match against Gabon on the 14th of that month. He substituted Djaniny at halftime. On 30 December 2013, Rodrigues appeared as a starter in the 1–4 loss against Catalonia in a friendly match, assisting his team’s goal that was scored by Djaniny. On 6 September 2014 he scored his first international goal in a 3–1 away win over Niger in Cape Verde’s successful qualification for the 2015 Africa Cup of Nations. Rodrigues was included in their squad for the finals in Equatorial Guinea, but due to competition from Kuca, Djaniny and Júlio Tavares he played only in the goalless draw with Zambia, which confirmed their elimination from Group B.

During the first half of the 2013–14 season Rodrigues scored 14 goals in total helping Levski Sofia to overcome several teams and progress to the 3rd place in the league ranking. He also scored a penalty in the 7-6 win after penalties against CSKA Sofia in a Bulgarian Cup Eternal Derby third round tie, eventually helping the team to reach the quarter-finals of the competition. The strong overall performance led to the interest of several European clubs. In January 2014, West Ham United sent an offer to Levski for a trial, but Rodrigues refused it, stating that he would only negotiate with a team which is guaranteed to offer him a contract.

On 27 January 2014, Rodrigues signed with Elche CF on a six-month loan through Promoesport (an investment fund linked to Gimnàstic de Tarragona), with a buyout clause. He made his La Liga debut on 1 March, coming on as a second-half substitute in the 1–0 home win over Celta de Vigo, and scored his first goal in the category on 3 May, netting the game’s only in an away success against Málaga CF.

In the 2014 summer Rodrigues signed a four-year deal with the Valencian club, after his buyout clause was activated. On 31 July 2015 he rescinded his link.

On 4 August 2015, Rodrigues signed a three years’ contract with PAOK for an undisclosed fee. On 23 September 2015, in a home derby game against AEK Athens he scored his first goal in Greek Super League. On 11 January 2016, PAOK turned down Al-Ahli Saudi FC’s offer in the region of €1.7 million for Garry Rodrigues. He finished the season with 7 goals being the third scorer of the club. On 24 November 2016 in UEFA Europa League group stage away match against ACF Fiorentina in the dying seconds Rodrigues storms downfield, cuts in from the left and fires into the roof of the net, giving his club an incredible 3-2 win.

On 9 January 2017, PAOK officially announced the transfer of Garry Rodrigues to Galatasaray for a fee of €3.7m. The transfer has been announced, thanks to the contribution of the 27-year-old player for so long. He is contracted to Galatasaray until the summer of 2021.

On 6 January 2019, Rodrigues joined Al-Ittihad of Saudi Arabia for a fee of €9m.

On 13 July 2019, Fenerbahçe announced the signing of Rodrigues on loan for 2 years from Al-Ittihad.