I have been in recruiting and specifically corporate recruiting for past 10 years. Major does not play a big factor in getting into recruiting. We tend to look for people with a passion for people as ultimately that is who you will be interacting with. To me recruiting takes a strong work ethic and customer service mindset to be successful. Your customers will be internal (hiring managers, business partners) and external (candidates) so understanding a customer mindset is vital to being successful. If graphic design is a passion I would suggest looking for a recruiting role or company that hires a lot of graphic designers, that way you include your passion along with your desire to get into corporate recruiting!
I echo a bit of the above! I'm in corporate recruiting and often in my role find opportunities that requires creative juices – talent & company branding. Your experience in graphic design will really up-level your team and company in these situations.
Additionally, a good point above, aligning with a company that is design focused might offer the opportunity to hire artists/designers where you experience would really give you a leg up.
If you land in a company with a corporate culture that allows you to wear multiple hats, you can definitely emphasize your graphic skills as an extra value. I have supported many facets of HR from a communication standpoint and they also need design for annual enrollment, benefits brochures, newsletter templates, etc.