In 2009, Ortiz signed for Paraguayan Primera División club Olimpia. He was named captain for the 2013 Season. After outstanding performances with the Paraguayan national team and Olimpia, he was linked to several teams in the summer of 2013. Among the teams were Mexican side Deportivo Toluca where his former coach and Paraguayan international José Saturnino Cardozo requested his services. Other sides from around the world, including Italian teams AS Roma, Genoa C.F.C and Bologna F.C., Premier League side West Ham United, Ligue 1’s Toulouse FC, 2010 Champions Olympique Marseille, 2011 Champions Lille OSC, 2012 champions Montpellier SC and Argentinian giants Boca Juniors were reportedly interested in signing the midfielder. Olimpia finally agreed a US$2.5 million transfer to Deportivo Toluca, which Ortiz also accepted.

On 11 October 2011 he made his debut for the Paraguay national football team and also scored his first goal for his country in a 2014 World Cup qualifier match against Uruguay.

On 28 May 2013, José Saturnino Cardozo (actual manager) announced that Richard Ortiz would join Deportivo Toluca. The club agreed to sign Ortiz in a 5-year contract for US$2.5 million. Ortiz would be the fourth Paraguayan in the squad joining then compatriots, Paulo da Silva, Edgar Benítez, and Pablo Velázquez. He scored his first goal for the Red Devils in the second match of the season against Monarcas Morelia. On 28 December 2015, Deportivo Toluca announced the return of Ortiz.

On 11 June 2015, Dorados de Sinaloa announced via Twitter that they had reached an agreement with Toluca to sign Ortiz on loan in a 6-month contract. At that time Richard was concentrated with the Paraguayan national team in Chile to play the 2015 Copa America, According to media, he let know his teammates his disagreement of playing with Dorados, the newly promoted team of the Liga MX.