win sbaround / over / round (to sth) to get sb’s support or approval by persuading them that you are right: She’s against the idea but I’m sure I can win her over.
sth is acceptable but wouldn't "someone" be unacceptable? Is over more preferable to "around"?
“I am sure I can win her over.” is perfectly right. Win over is the correct phrasal verb though win round is some times used but I would not prefer the preposition round. Win over being a transitive phrasal verb, is separable and as such the object can be placed between the verb and the preposition or after the preposition if the object is not a pronoun
So you can saY: We'll be working hard over the next ten days to win over the undecided voters. I hope I can win them all over to our side. I won over the mayor to our side.