It happened around 12:20 p.m. A security camera picked up the suspect who was taken into custody, police said.
Joyce is being held on $100,000 bond.
The rapper no longer lives in the mansion and has been trying to sell it for over a year.
In July, he dropped the price of his mansion once again after a bankruptcy judge approved a plan to reorganize his finances. According to Zillow, the hip-hop mogul cut the asking price of his 50 Poplar Hill Drive home to $5.995 million. It was dropped by $2.5 million.
50 Cent, whose real name is Curtis Jackson, III filed for bankruptcy in 2015.
In July, Jackson appeared in bankruptcy court in Hartford. A judge approved a plan for him to reorganize his finances and pay back creditors.
The 21-bed, 35-bathroom property was listed at $8.5 million in October 2015.
The rapper and businessman originally tried to sell the mansion for $18.5 million in 2007.