Born in
Cagliari, Murru started his career at hometown's
Cagliari. In July 2011 he was promoted to first team squad, and played his first match as a professional on 20 December, coming on as a second-half
substitute in a 0–2 home loss against
Milan. Murru appeared in only one further match during
the campaign, a 0–0 draw at
Fiorentina, also from the bench. In 2012, after
Alessandro Agostini's departure to
Torino, he acted as a backup to
Danilo Avelar. In the following year Murru appeared as first-choice, overtaking Avelar in the pecking order. On 8 October 2013, he renewed his link with the
Rossoblù, until 2017. On 1 July 2017, he joined
Sampdoria. On 17 September 2020, Murru joined
Torino on loan with an option to buy. ==International career==