Normally, you cannot track a job application process. If you make an online application, you will normally receive a confirmation email informing you that your application has been received. The email is normally automated so there is no need to reply in most cases. The confirmation email will normally mention something along these lines: “Dear Applicant, Thank you for your interest in a career at StudentJob.
We have received your application for the online marketing intern position. We will review your application and get back to you as soon as possible. Please note that because of the high number of applications we will only reply to those who will be shortlisted.”
If they don't get back to you, then that might mean that you weren't successful this time or they had so many candidates applying to the postion that they didn't notice your application. Don't give up!