Reform Scotland said staying in touch with loved ones while behind bars would help reduce the risk of re-offending.
In a report published today, the think tank also calls for a ban on sentences of less than six months and an end to automatic early release for those serving short jail terms.
Reform Scotland said prisoners are currently restricted to using phones outside their cells or receiving print outs of e-mails.
It called for a pilot scheme that would see landlines installed in prisoners’ cells, which already happens in some prisons in England and Wales.
Research director Alison Payne, said: “Prison exists for four key reasons – punishment; deterrence; public safety and rehabilitation.
“The fourth, rehabilitation, does not always receive the attention it deserves. However, rehabilitating prisoners and preventing re-offending is important not just for the prisoner, but also for his or her family and for society.
“If family contact helps to reduce reoffending, as well as helping those left outside, then it is something that needs to be encouraged. Reform Scotland believes that there should be some pilots looking at innovative ideas for increasing contact, such as having landline phones in prison cells.
“We challenge the Scottish Prison Service and the Scottish Government to be bold as we try to close the revolving door of reoffending.”
Nancy Loucks, chief executive of Families Outside, a charity which works to support the families of prisoners, said: “Imprisonment fractures families.
“It separates people from the things most likely to prevent them from offending, such as housing, employment, and social support, increasing the risk of family breakdown, relapse, and homelessness.
“Community-based measures are designed to address the reasons behind someone’s offending while maintaining their links to their communities – something short prison sentences simply cannot do.”
A spokeswoman for the Scottish Prison Service said: “There are currently no plans to introduce in cell telephones in prisons in Scotland.
“The Scottish Prison Service recognises the importance of maintaining family links with a family member during their time in custody and continues to look at ways in which we can support and enhance this.”