Can my family claim me if I am a part time student and part time employee? I don't contribute to rent but pay for personal bills, WiFi, phone bill.

They can claim you if you don’t earn more then $4,300 and they provide more than half of your support. 

@Bsch4477 's response is not all inclusive, as there are other things that come into play here.

If on Dec 31 of the tax year you were:

Under the age of 19 and *YOU* did "NOT" provide more than 50% of your own support, your parents qualify to claim you. Period.

 ****OR****

- Under the age of 23 and;

- Enrolled as a full time student for *any* *one* *semester* that started during the tax year and;

- were enrolled in a course of study that will lead to a degree or credentialed certification and;

- were enrolled in a qualified institution and;

- did not provide more than 50% of your own support for the entire tax year, then

Your parents qualify to claim you.

Take note that the support requirement is on the student - not the parent. There is no requirement for the parent's to provide you any support. Not one single penny.

Take note that your earnings don't matter. If either of the above scenarios fit, then you could earn a million dollars and your parent's would still qualify to claim you.

Final note: The key word here is *QUALIFY*. It does not matter if your parent's actually claim you or not. If they "QUALIFY" to claim you and you are required to file a tax return, then you are required to select the option for "I can be claimed on someone else's tax return."  Again, it does not matter if your parent's actually claim you or not.

@Carl11_2 makes the point that the rules for dependency are complicated. Just to be clear and to simply, from your post I assume that you are older than age 18 and, as you posted, you are not a full time student. In that case the only way you can be claimed is, as I posted, for you to be known as what the IRS calls a qualifying relative. You qualify if you do not earn more than $4,300 and if your parents provided more than half of your support. Note that for the qualifying relative it is the parent who must provide the support. This is not the case, as @Carl points out, for the qualifying child which you do not qualify for if my assumptions are correct.