The con, which has just come to light, involves an e-mail that claims to be from HM Revenue and Customs but comes from an msg.com address.
One woman received an e-mail informing her that she was eligible for a £397 tax refund and directed her to a link to a "refund form," bearing the official HMRC logo.
She said: "I thought you wouldn't get an e-mail from the tax man out of the blue like that.
"The e-mail address was a bit strange looking although the refund form looked genuine.
"Because it asked for my bank details I got suspicious and didn't take it any further."
The e-mail - which is addressed to 'Dear Customer' - claims the recipient is entitled to a tax refund following "the last annual calculations of your fiscal activity".
It states: "Please submit the tax refund request to unlock the 397.65 GBP.
"To access your tax refund, please download the form attached to your e-mail and confirm your details.
"If you have already confirmed your information then please disregard this message."
It even goes as far as to warn people not to reveal their bank details over the telephone.
A spokesman for HMRC said they would never contact anyone via e-mail.
He said: "People should be alert to anything unsolicited that asks for bank details. We would never contact tax- payers by e-mail".
A spokeswoman for Police Scotland said: "We would always advise people not to give personal information details in response to unsolicited e-mails and always double check the address of the sender".
She said more advice was available at www.staysafe online.org or www.action fraud.police.uk