In U.S. Corporatese, I would suggest saying "I'll outsource this task/project/job" if referring to a specific "job". Saying "I'll outsource my job" sounds like you're not going to have a job anymore, and that you're responsible for replacing yourself!
In some professions, it is common for funcionários terceirizados to be under independent contract (i.e. A contract with the person directly, with no other company involved), and they often end up being called "contractors". This is particularly common in the engineering offices I have worked in. "Go see if one of the contractors can help you with running this test."
And the word "third" is definitely incorrect on its own, but Daniel's suggestion of "third-party" is frequently used as well to refer to the hiring process for temporary laborers. We frequently have to hire extra help that way and we call it "hiring via third-party" or we say "yeah, we'll have to hire them through a third-party". But, as mentioned by Flavia, third-party can be used quite broadly. For example, our customers frequently hire "third-party inspectors" (called "TPIs" around the office) to be official witnesses to the work we are performing.