Not as such, no.
The problem comes from the fact that your mobile device has no browser, and MySpace does not allow a third-party to proxy log-in requests. Your App could bounce a browser to MySpace, have the user sign-in, then bounce back to your App with a token, but it still requres the user to enter the information directly into the MySpace website. You can't automate that.
However, there is an alternative, and due to the security limits placed on the RESTful API, it's not onerous. It requires three parts, though. First, the mobile application that will interface with the user; second, a server which will handle a seperate login mechanism (not a MySpace login, your App's own), third, a MySpace App that must be installed on a User's account to allow access to their data RESTfully.
Let's pretend your mobile application is called MyMobileSpace (note: you cannot use that name - it violates the ToS; this is just an example), and it's counterpart MySpace App is called MyMobileSpace Enabler. When the user installs MyMobileSpace Enabler on their account, it asks them to create a login for MyMobileSpace (or to link to one they already created). You can have it ask for some username and password combo; once they do, you send that information, along with their MySpace userId, to the server that handles the login.
Now, when they run MyMobileSpace on their mobile device, it'll ask for their login info. They get connected to your server, which looks up their MySpace userId based on that login info, and can then use that Id to request resources from the RESTful API -- all without ever having to actually log on to MySpace itself.