Can my Uber cross the Mexico Border? The Mexican border to Tijuana for example.

No. Historically, there was UberPassport...now discontinued.

No, you cannot.  Uber does not currently alllow drivers to cross the border for various legal reasons.  In the past, Uber made a special case, called UberPassport, where a rider request such a service, say from San Diego to Tijuana.  This was limited to drivers who participated and there were extra fees.  However, this has now been discontinued.  Here's the statement from Uber:

The UberPASSPORT pilot product was discontinued on September 1, 2016. For trips to or from Mexico, take an Uber to the border, cross, and request on the other side. 

If you want to find out more about the history of UberPassport, check out these artices:

http://abcnews.go.com/Business/uber-mexico-back-us/story?id=37752343

https://newsroom.uber.com/us-california/connecting-sister-cities-at-the-tap-of-a-button/

UPDATE: Many drivers have indicated that this is up to driver discretion, and that many drivers do cross the border.  This seems to be more common in areas like Detroit and Buffalo, however.

ippei 1202

Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC