Graphic designers are trained not only on software such as Adobe, but more importantly are trained as visual problem solvers with a foundation in visual arts. Anyone can do tutorials or train on the technical side of the software, but developing the creative capacities to successfully apply the software to visual problem solving is what's vital to graphic design. You can certainly apply for the position, but know there is a good chance the company is looking for someone who is ready to create products such as professional looking flyers or a newsletter. You can certainly apply but be honest about your skillset or you will waste your time and theirs.
I suggest that you research IT managers using professional networking websites, and reach out to some of them. Discuss your availability as an intern with a focus on your skills and the tasks that you are ready to help them complete. They may not have considered an intern for their particular department, and may realize you are a good match for certain projects. Timing is vital, so be ready to continue submitting resumes and a great cover letter over a period of time. You may be able to start in an entry level job role instead of as an intern, but may still be eligible for internship credit through your college (if you even need that). All the best to you!