Police were called after the unnamed man turned up at Moore's home in Hollywood, Los Angeles, on February 12. He was trying to leave notes on her doorstep and then became unsettled.
The 31-year-old singer, who was home at the time, was allegedly subjected to screaming and swearing from the suspected stalker.
It's reportedly the third time in as many days that the man, believed to be in his 40s, has arrived at the property unannounced and uninvited.
When he showed up the first time Moore called the police, but the man was not arrested.