You can't get an accurate position as the SERPS differ from region, however is there a way to find your average position for a specific query? for google.

Regions, data centers, localization identifiers etc. There's so many things that can change how the SERP's end up for a user. So the average position isn't really possible to get in a way that it has value because you'd need to mix it with the user count / traffic etc.

But you can look up the positions: http://oy-oy.eu/google/world/

http://www.reladvance.com/metrix/find_metrics_form.php