Yes it is. You have the correct definition of brush up. However, that statement is incomplete. Notice that brush up has no object. There's just a lingering "my". Also, the "--" indicates that his thought or speech was interrupted.
According to the article
While greeting Grande at the Greater Grace Temple in Detroit, Michigan, Ellis said, "I’ve got to apologize because I have to brush up my -- my 28-year-old daughter tells me, ‘Dad, you are old at 60.'"
“What did you do? What happened?” Grande asked with a laugh.
"When I saw Ariana Grande on the program, I thought that was a new something at Taco Bell,” Ellis explained to the crowd. “Girl, let me give you all your respect.”
Returning to the incomplete sentence, there are many possible ways to reconstruct it, but given the context, my interpretation is that the complete sentence is something like
I’ve got to apologize because I have to brush up my [knowledge of {celebrity names | pop artists | younger artists | etc. }].
Ariana Grande is a young artist who appeals to a younger audience. So Ellis is joking that he's so old and out of touch with current music that he didn't know who Grande was and that mistook her for a Taco Bell menu item. For context, grande happens to mean big in Spanish and Taco Bell serves (so-called) Mexican food. An item on their menu could conceivably be called grande.
For what it's worth, I would have said "brush up on my...", but that's likely a personal preference.