Career
Born in Sassari, Sardinia, Burrai started his career at Sardinian club Cagliari. He made his Serie A debut in the last round of 2006-2007 Serie A.
He left for various Serie C1 clubs from 2007 to 2011, with Foggia also received half of the registration rights for a peppercorn fee of €500. In June 2011 Foggia bought Burrai and Marco Sau outright for €207,000.
However, on 31 August 2011 they were bought back from Foggia, for €207,000 (Sau) and for free (Burrai).
In January 2012 Burrai was signed by Latina, again in co-ownership deal for €500. In June 2012 Cagliari gave up the remain 50% registration rights.
On 31 August 2013 Burrai was signed by Serie B club Modena, with Alberto Massacci moved to Latina in temporary deal. On 3 July 2014 Burrai was signed by Serie C club Monza in a 3-year contract.
On 22 December 2014 Burrai was released.
In January 2015 he was signed by Juve Stabia in a 1½ year deal. On 28 July he was signed by South.S. Robur Siena on a free transfer.