Marc Alcalá first took part in national championships in 2011 and was the Spanish U18 champion over 1500 meters. A month later, he also competed over this distance at the U18 World Championships in Lille, where he was eliminated in the preliminary run. A year later, at 17, he started in the older age group at the U20 World Championships in his hometown. After he had already won the national U20 title, he was eliminated in the preliminary stages of the World Championships and finished 33rd in 3: 55.68 minutes. Another year later he ran at the U20 European Championships in Rieti in a time of 3: 51.17 minutes in 18th place. Before that, he already competed in the U20 race of the Cross Country World Championships in Bydgoscz in March. In 2014 he became the Spanish U23 champion and later also won the gold medal over 1500 meters at the U23 Mediterranean Championships.
In spring 2015 Alcalá took part in an international adult championship for the first time at the European Indoor Championships in Prague. With a lead time of 3: 50.46 minutes, he finished 25th. In the summer he won the gold medal at the U23 European Championships in Tallinn. At the World Indoor Championships in Portland in 2016, he was eliminated in seventh place in his preliminary run. He caught the significantly faster forerun, which is why he 'after adding the two forerunners ended up in 10th place overall. in the summer he finished 22nd at the European Championships in Amsterdam. Before that, he was the first national champion over 1500 meters for adults. In 2017, after his title in the open air, Alcalá was crowned the Spanish champion over 1500 meters indoors for the first time. In March he was able to celebrate his greatest sporting success with fourth place at the European Indoor Championships in Belgrade. He could not build on this performance in the summer at the World Championships in London after he was eliminated as tenth of his preliminary run. Also in spring 2017, he finished eighth with the Spanish mixed relay at the World Championships in Kampala.
In 2018 he failed at the World Indoor Championships in Birmingham as fourth of his run just short of making it to the next round. At the summer Mediterranean Games in Tarragona, he finished 13th.