WPA (Win Probability Added) does what you are looking for, although with some limitations. WPA takes the difference in win expectancy for each team for each play and assigns it to the pitcher (for the defense) and the batter (for the offense). Since both pitching and hitting components are measured, a pitcher's contributions both on the mound and at the plate can be considered. I'm not aware of any site that actually combines those two numbers, but it's easy enough to just add it up.
The highest offensive WPA contribution for a pitcher of 2015 was Steven Matz's game on June 28 against the Reds (according to Baseball Reference Play Index). He went 3-for-3 (2 singles and a double) driving in four, which added up to 41% WPA. He also pitched 7.2 innings giving up two runs, which accounts for another 12% WPA. So total, he contributed 53% WPA to the Mets that game. Not bad for a Major League debut.
A couple of things to keep in mind about WPA. On the defense side, all of the value is attributed to the pitcher. So if a fielder makes a great play, the pitcher gets all of the credit. Also, it's all about context, so closers tend to have really high WPA values because they come into games that could go either way (~50% win expectancy), and if they close out the victory (100% win expectancy), the WPA will be ~50%. In a blowout, it's difficult to gain (or lose) WPA because the outcome of the game is largely determined already.
See Fangraphs for a good summary of WPA.