I received a w2 from a part time job and only made $270 in 2016. Do you have to make a certain amount before you have to claim?

You can see if you are required to file a federal tax return by reading the TurboTax FAQ below:

https://ttlc.intuit.com/replies/3302274

If you have to file and are asking whether you have to bother adding the $270 to your return, the answer is "yes, all income has to be reported".