The 23-year-old Leicester lock, 6ft 8in and 19st 5lbs, qualifies for Scotland through his Glasgow-born father and impressed Hadden last season when he was part of the Barbarians squad that came to Murrayfield in May for a game the Scots won 66-19.
Hadden said: "I'm keen to see how James fits in to our training programme.
"He's a big man and athletic with it and, as I've said already this season, competition for places is growing all the time and that's good as we gear towards the 2007 Rugby World Cup."
Hamilton, born in Swindon, played 24 times for Leicester last season, including two Heineken Cup fixtures and was part of the England under-19 squad at the 2001 Junior World Championships in Chile.
Now, however, he has decided to try to win a place in the Scotland set-up.
Hamilton said: "I've opted to try to play for Scotland because it's a personal decision from my heart.
"I like the way Scotland play and all I really want to do now is get involved with the lads at the squad session."
Hadden was given a boost when he was able to list Edinburgh back-row forwards Simon Taylor and Allister Hogg, who are both recovering from injury.
Taylor has been out since May when he damaged his knee playing against Connacht, while Hogg injured his elbow in the Magners League derby against Glasgow Warriors last month.
Hadden said: "Both Simon and Ali are making excellent progress towards a comeback and could figure during the autumn Tests.
"I'm very much looking forward to our matches next month against Romania, the Pacific Islanders and Australia.
"International rugby is back at Murrayfield and I know from speaking to the players that they're keen to build on what we achieved last season."