Police were called to Iceland in Havelock Square shortly after 11.30pm on Tuesday, December 30 following an alarm activation.
Officers found damage had been caused to a glass door and a cabinet containing alcohol inside the shop and it was cordoned off as a crime scene until Wednesday afternoon.
Descriptions of the suspects were passed to officers and they searched the area and arrested a man in his 40s.
They later charged the individual and named him as Dean Cochrane, 44, of no fixed address.
Cochrane has also been charged with stealing £350 worth of whiskey from Tesco on December 24, taking a charity bucket from Greggs in Havelock Square on December 28 and making off with alcohol to the value of £373.75 from Tesco in The Parade on December 29.
He has been remanded in custody ahead of a hearing on Wednesday, January 7 at Swindon Magistrates Court.
Wiltshire Police has confirmed that the second suspect “has not yet been arrested” but their enquiries are ongoing.
They have not released a description of the suspect they are searching for.
A spokesperson for the force said: “Anyone who witnessed anyone acting suspiciously in the Havelock Square area between 11pm and midnight [on Tuesday] night should get in touch.
 “Email 70059@wiltshire.police.uk and quote crime reference number 54250168698. Alternatively, call CrimeStoppers anonymously on 0800 555 111.”