| Yes, but it will probably cost you.
I had 'private' or 'blocked number' or 'unknown number' calling my home at all hours. My phone company said that I needed to hit a certain code on the phone, *000 (cannot remember the numbers now), and the call would be flagged.
But, I did not have access to the records, but could request them through the police department.
In my case, I believe each call was $3.50. | 
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