Police say the abuse occured between three and five years ago, when the girl was living at Megginson's home.
Megginson was arrested Monday night after being interviewed by police.
Megginson has been charged with four counts of rape in the first degree, one count of continuous sexual abuse of a child and one count of endangering the welfare of a child.
He has been arraigned and committed to the Howard Young Prison after failing to post $230,500 secured bail.
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