Can I Be Pregnant If My Period Is 2 Weeks Early?

Simply, yes. An early period is often an indicator of pregnancy. You might just be heavily 'spotting' however. This is common, and spotting severity differs with each woman. 'Spotting' is light bleeding, with the blood usually being darker than a period, even brown. The problem is it can be a normal occurrence or it can be a precursor to pregnancy.
The way to tell is to simply consult a pregnancy test. If this doesn't give you an answer and you don't develop any pregnancy symptoms but do continue to have your period then see your GP or doctor or visit a clinic. A medical professional is worth bothering for resolution and peace of mind. It could be pregnancy, it could be natural, or it could be a hormonal imbalance. A medical exam would tell which. You shouldn't feel embarrassed or that this is something not worth the hassle.
However, an early period doesn't mean you ARE pregnant. Psychological conditions such as anxiety, stress and fatigue can trigger an earlier period. This isn't necessarily a bad thing, rather an indicator that you need to alter your lifestyle. Again, a doctor will be able to advise remedies. It could be a diet change, or an increase in exercise, or a change of work. Altering the factors will alter the problem.

You may be spotting if it is not a regular period. If this is the case then you can be pregnant. But to be for sure, you must take a pregnancy test as soon as you miss the date of your period.

Early period can also because of some hormonal imbalance but these things can also be defined once you take the medical examination.

Can I be pregnant if my period is a week early?

Yes you would just have to go and get checked out cause that might mean something's wrong with your baby or you should go get checked out now...