There is currently no way to initiate a scan via the API. Please have your Account Manager put in/add you to a Feature Request for that functionality.
Well, it gets quite a bit less embarrassing when you consider that a triggered scan, after the initial install, is basically not necessary with AMP. Because we're continually monitoring the activity on the endpoint, anything bad should get picked up. Stuff that initially passed muster and later is identified as malicious is handled by AMP's retrospection feature.
AMP does an initial scan at install time (by default) to pick up anything that was already lurking on the endpoint prior to AMP installation. Once you've done that the first time, there is very little benefit in continually re-scanning clean files over and over. All it really does is chew up system resources.
For customers who need to scan because of overly-restrictively-written policy requirements, scans can be scheduled via the admin console. But we pretty much never recommend doing so unless you absolutely have to.
What's the scenario you have in mind for API-initiated scans?