Project Manager- How to get team member to use his calendar software

Use feedback. Do not enable his one-off behavior.
Many years ago I had a corporate artificial intelligence position where there were thousands of employees on site and at least a couple hundred in my division. The *only* way meetings were scheduled was through the corporate calendaring system. You literally did not know the meeting existed unless you used the calendaring system.
It could sound like "Hey Bob, can I give you some feedback?" ... "When you miss important meetings you look less organized and team performance suffers...what can you do differently." If Bob pushes back about no one checking with him on *his* mental calendar then you can respond "I see. What can you do differently?"
It is not efficient for everyone to agree to a meeting time and then say "Ok, and what about Bob?"

I'm the project manager, not direct manager and I'm in week three of the job. So I'm needing to find a more politically nuetral way to do it. I guess once I'm more established in the role I can roll out some PM Feedback, but if I do that right it will be six months before I am using negative feedback.
Thanks though, feedback is probably one of the best solutions.
 

I'd go with a focus on the results and why you need him to do it.
Is the need really for him to use the calendar? Or is the need for your admin to be able to schedule meetings at a time when everyone is available?

and how important is this project? 
I get the sense that your project isn't important - to him, at least, and probably his manager.  If he's going to offsites while you're trying to get out of concept phase, maybe his offsite is more critical.  Or maybe he's just playing power games.  
And maybe, your project doesn't need him.  Try going ahead without him.  Schedule the meetings, hold them, give the key assignments to those who are actually committed to the project.  
It's the very rare engineer who is irreplaceable.   Even if we think they're "gifted" they can be replaced.  
[edited to add]  I'm not saying kick him off the project.  Rather, make decisions in meetings without his input.  Assign cool tasks to those who are at the meetings.  It's likely he'll want to be a decision maker and a go-to guy, and he'll really want to be in those meetings.  I know it's a bit of a political game, but if you have no power over him and he persists, there may be no other way.  
John Hack

First, try peer feedback rather than feedback designed for the direct (http://www.manager-tools.com/2006/10/the-peer-feedback-model) 
Second, make sure your meetings are in fact adding value, and that you're inviting people who need to be at them.   He may have been invited to lots of time-wasting meetings, and is avoiding yours based on past experience.  If your meetings are sharp and well run, he may be more willing to attend.  
John Hack

Thanks for all the input, nice to bounce the ideas of other profesionals to validate my thought process.
1- I'm going ahead with the meetings. I almost always schedule them a week ahead of time.
2- I publish clear meeting minutes (MT style, who does what by when).
3- I'm following the Effective Meetings process. Agendas, start on time, end on time, etc.

I agree with others, you need to proceed without him and give him feedback about not being difficult to colalborate with.  You shouldn't have to chase him down.  If he doesn't attend meetings that is more feedback, you miss his input on important decisions, you don't know where he is on tasks, you don't know if you can assign him tasks.