Basically what you're saying is you want to be able to have a user who is logged into your site be able to click a link to the "add application" page for your app, add the app, and based on params from your site the app will know who the user is that added?
As far as I know, there is not. What you can do is just have the user log in once the app is started using the same credentials as are used on the site. Then you would just pass that to your site, check the credentials and then send back the users content or do whatever.
Having the user log in again is also a lot more secure. If one of your users left the page open with the link to the myspace app, any person who came along could represent their myspace to your site as the users myspace, and access their stuff.