Does it have to be the camera image that must be clicked?
You can specify a URL to go to when the web part title is clicked. Edit the web part properties and look under the Advanced section, for Title URL.
Another way I have done this is to put a Content Editor web part under it with an anchor tag that says something like "Click for Full Screen" and the anchor tag would go to the URL of the webcam viewer.
Beyond that, you would need to use a Content Editor web part or Script Editor web part and create the iframe yourself and handle an onclick event. Very dependent on how your webcam works, if it's even possible. (That's about all the Page Viewer web part does - creates an iframe.)