A Canadian woman who served in the Israeli army and spent time in a US jail for fraud has been identified as the first foreign female fighter to join Kurdish militia fighting Islamic State (Isis) jihadists in Syria.

Gill Rosenberg, 31, from White Rock, near Vancouver, British Columbia, said she travelled to Iraq to receive training and join the Women Protection Units (YPJ) - the all-women Kurdish militia - with which she was now battling Islamists in neighbouring Syria.

"They [the Kurds] are our brothers. They are good people. They love life, a lot like us, really," she told Israel Radio.

Rosenberg, a civil aviation pilot, reportedly grew up in Vancouver before relocating to Tel Aviv, where she enlisted in the Israeli army search-and-rescue unit.

In 2009 she had a run-in with the law, as she was arrested and extradited to the US over an international phone scam, according to one of her lawyers.

The FBI accused her being part of a gang running "a phony 'lottery prize' scheme that targeted victims, mostly elderly," according to her case file. Another 11 people were arrested for their alleged involvement in the scheme.

Rosenberg entered a plea bargain and served three years behind bars.

She said she recently got in touch with Kurdish guerrilla fighters online and decided to join them.

The cover photo of her Facebook profile features the International Airport of Erbil, a Kurdish city in northern Iraq.

In a recent photo album, she can be seen in mountainous regions of Syria and Iraq, while in one of her last postings she seemingly vows her readiness to fight Islamic State extremists.

"In the IDF [Israeli army], we say 'aharai', After Me. Let's show Isis what that means," the post reads.