Yousif Badri, 29, is accused of being involved in conduct "with the intention of committing acts of terrorism".
The medical student denies charges under the Terrorism Act at the High Court in Glasgow.
The trial was told Inspire is a glossy magazine about al-Qaeda's philosophy, including how to make bombs.
Dr Matthew Levitt, who formerly worked for the FBI, told the court he did not know that the magazine was on the US Navy website.
Cross-examined by defence QC Murdo Macleod, Dr Levitt said the magazine was freely available on the internet.
He added: "There is no Inspire website as such, but the material can be posted on a variety of websites.
"Today if you were to do a Google search you would find them right away."
The offences are alleged to have been carried out at two places in Aberdeen - Mr Badri's former flat in Ashgrove Road, and in Berryden Retail Park.
The trial, before judge Lord Turnbull, continues.
An al-Qaeda magazine called Inspire which was found on a hard drive in an Aberdeen flat is available on the US Navy website, a trial has heard.