Born in Yecla, Region of Murcia, Ortuño graduated from Albacete Balompié's youth setup. On 20 December 2008, while still a junior, he played his first match as a professional, coming on as a second-half substitute in a 0–3 away loss against UD Las Palmas for the Segunda División championship.
In the 2010 summer, Ortuño was definitely promoted to the main squad, but appeared rarely as the Castilla-La Mancha club dropped down a level. On 11 July 2011, he moved to Getafe CF B in Segunda División B, and continued to compete in that level in the following seasons, representing Levante UD B and La Hoya Lorca CF.
Ortuño joined Granada CF from La Liga on 17 January 2014, being immediately loaned to Girona FC. He scored his first professional goal on the 25th, netting his team's only in a 1–1 home draw against SD Eibar; he finished the campaign as club top scorer alongside Gerard Bordas, as the Catalans narrowly avoided relegation from the second level.
On 28 July 2014, Ortuño signed a new deal with Granada running until 2018. He played his first game in the main category of Spanish football on 23 August, featuring 45 minutes in a 2–1 home win over Deportivo de La Coruña.
On 16 January 2015, Ortuño was loaned to Las Palmas until June. After the club's promotion to the top division, he was bought outright for €1 million, signing a contract until 2019 but being loaned to Real Zaragoza in the second tier on 21 July.
After an unassuming six-month spell at RCD Mallorca in 2016, Ortuño joined fellow second tier club Cádiz CF on 4 August of that year, on loan for one year. He scored a career-best 17 goals for the side, including braces against Getafe CF, AD Alcorcón and Córdoba CF.
On 2 September 2017, Ortuño cut ties with Las Palmas, and signed a one-year contract with Real Valladolid the following day.
Ortuño's younger brother, Juan Tomás, is also a footballer and a forward. He too was brought up at Albacete.