It's not possible to get an actual count. There's nothing on your profile that will give this information.
However, there's a Data Explorer query that will give you a list of eligible posts that, if you upvote, will count towards the badge.
So the only way to get a number is to run down this list and count up how many you have upvoted.
Note that it's not possible get an actual progress indicator since votes are anonymized. So the data explorer cannot determine how many of them you have actually upvoted.
As a final disclaimer: Do not abuse this query to serially upvote everything to game the badge.
IIRC, I've seen somebody suspended for voting irregularies while having "Sportsmanship" as the most recent badge.