The star took to Twitter on Tuesday to invite her out for a drink.
"Dear @rihanna, pardon my inane self indulgence. Let's have a drink someday (on me)...," he wrote.
The 51-year-old actor was previously involved in a Twitter feud with the Work star after she reportedly shunned his request for her to meet with his then-fiancee Scottine Ross because she was a big fan.
Asked if they had resolved their differences from three years ago, Charlie told Andy Cohen last week: "Oh, that b**ch."
When Andy noted he may have just made the situation "worse", he replied: "No, she abandoned common courtesy and common sense."
Despite his previous erratic ways, the Mad Families actor - who has kids Cassandra, 32, Sam, 12, Lola, 11, and seven-year-old twins Max and Bob from past relationships - also told the host he isn't as "insane" as people think.
Asked the biggest misconception about him, he said: "That I'm bipolar or insane - I'm actually quite thoughtful and often times rooted in all things logical."
And Charlie, who confirmed last year he is HIV positive, revealed his health is "really good" at the moment.