Can I call a professor to ask for a letter of recommendation if I can't show up in person? I am applying for a PhD. There is a professor at my undergraduate institution I would like to ask for a LOR. I emailed him, but after a full week he has not replied.

From this I can infer that either he doesn't want to write the letter, or he is behind on email. I have to hope it is the latter, since he is the only professor I did research with, therefore my application would be much weaker without his letter. If he is behind on email, I have no way to tell how long it might be before he will see my email.

I would have gone in person, but I live very far away and cannot easily visit his office. Should I phone his office and:


leave a message?
phone during his office hours so I know he'll be there?


Applications are not due for approximately another two months; should I just wait a few more weeks before asking someone else for a (weaker) letter?
In general you should not call a professor unless they are expecting your call, or have a very close relationship with you (if they did, you would know).  The social convention is to send him a followup email reminding him of your request.