The 23-year-old joined Barrow at the start of the season from Stenhousemuir but made only six National League appearances for the Cumbrian side.
Murray began his career at Scottish club Motherwell and also had spells with Arbroath and Clyde.
Southport are 19th in the table, two points above the relegation zone.

Tariq Hameed Karra described government policy as "brutal" and condemned his People's Democratic Party for its state-level alliance with the BJP.
He quit his party and resigned from parliament.
More than 80 people have been killed since wide-scale riots erupted in early July.
The mass closure of mosques in Kashmir hampered the festival of Eid al-Adha this week.
"For the first time in history, the people of Kashmir were not allowed to offer Eid prayers. Certain shrines and even the Grand Mosque were locked,'' Mr Karra told reporters on Thursday.
"Kashmiri blood is being spilled on the walls, lanes and drains of the valley," he added.
The demonstrations were sparked by the killing of a popular militant leader, Burhan Wani, 22, in a gunfight with the army.
Disputed Kashmir is claimed in its entirety by both India and Pakistan and has been a flashpoint for more than 60 years, causing two wars between the neighbours.
Within the disputed Muslim-majority territory, some militant groups have taken up arms to fight for independence from Indian rule or a merger with Pakistan.

The inquest is looking into the murders of ten Protestant workmen in the County Armagh village.
Earlier, coroner Brian Sherrard said police should be given time to pursue a new lead that emerged last week.
A partial palm print, found on a getaway van, was re-examined and, for the first time, linked to a suspect.
Mr Sherrard said that, given the significance of the evidence, the PSNI should be allowed the opportunity to investigate it.
"My obligation to the deceased, to the families of the deceased and to the community as a whole, and in the interests of justice, demand that the police be allowed the opportunity to investigate this new lead.
"That, however, cannot be an open-ended opportunity," the coroner said.
"I am acutely aware that more than 40 years have passed since the attack and that those closest to the deceased require answers while they are fit enough to participate."
Judge Sherrard said the discovery of the print had "shaken the confidence of a number of families who now wonder who to believe and what they can believe."
He said this was "quite understandable given the timing".
"These families wish the inquest to push on despite this development as they see it as the best way for them to gain an insight into the deaths all those years ago," he said.
But he argued that the discovery of the palm print was likely to prove "invaluable" in allowing the inquest to answer key questions.
"This is the first and best opportunity since 1976 to establish a verifiable link between the person who has been identified and the attack. That link may produce many more leads," he said.
The coroner said a timetable would be put in place and that families will be advised as to the progress of the investigation.
The ten men were taken from their minibus as they made their way home from work at mill in Glenanne and shot dead by IRA gunmen in January 1976.
One Catholic man was allowed to escape.
No one has ever been convicted over the atrocity.
Deputy First Minister Martin McGuinness, Sinn FÃ©in, said it was absolutely incredible that it took somebody 40 years to come up with the palm print finding.
He was asked about the situation at a meeting of the Assembly's Executive committee on Wednesday.
However, after he said he was surprised about the palm print, the committee chairman, Ulster Unionist leader Mike Nesbitt, asked him not to say anything else in case it was sub judice.
The inquest is expected to resume on 21 June.
Southport have signed defender Euan Murray from fellow National League club Barrow on a deal until the end of the season.
[NEXT_CONCEPT]
An MP from the ruling party in Indian-administered Kashmir has resigned to protest against the way authorities' have handled weeks of political unrest.
[NEXT_CONCEPT]
An inquest into the 1976 Kingsmills massacre has been adjourned until later this month.