A Canadian-born immigrant to Israel has become the first foreign woman to join Kurds battling Islamic State in Syria, a Kurdish source said on Tuesday, as details surfaced of the volunteer's turbulent past.

Gill Rosenberg, 31, is a civil aviation pilot who enlisted in an Israeli Army search-and-rescue unit before being arrested in 2009, extradited to the United States and jailed over an international phone scam, one of her former lawyers said.

Contacted on an Iraqi cell phone number, Rosenberg told reporters that she was in Syria, but declined to comment further: "Sorry, you have to go through the chain of command in YPJ," she said, referring to the Kurdish women's militia she has joined.