Baseball-Reference, among its many awesome things, has a current attendance page.â†µ
And according to that page, through the first three games, the Rangers were the most attended team, per game, in baseball. They're up nearly 19,000 per game from this point last year.â†µ
Really small sample size and the Red Sox obviously helped, but cool, none the less. I’ll be interested in keeping track of this as the season goes on.â†µ
UPDATE: Playing the Mariners already dropped them to fourth. Thank you small sample sizes. They are still first in per game gain, though, by quite a bit.