Yes, you can. FragmentActivity is a subclass of Activity, which has the "startActivity" public method. You have to call that method from inside of onCreate, for example.
FragmentActivity | Android Developers
Edit: If your fragment is contained in the Activity class (i.e. is an inner class) you can use ActivityClassName.this as the first argument, otherwise, if you need to access your main activity from a Fragment class that has it's own file, you can always use the Fragment's getActivity() method as the first argument.