A traditional college recruiter is one who recruits for undergraduate and graduate programs and this not a "human resources" kind of role at all. In fact today's college recruiting environment has become much more about marketing, analytics, and digital media. Recruiters are looking to find students who may be a fit for their institution and use a variety of outreach tools to connect with them. Refer to the "admissions funnel" for more information on this.
As I said, recruiting has become much more about marketing and this is not an HR professional kind of role. Someone who can market programs, write well, speak well in front of groups, and analyze metrics can excel in today’s college recruiter role. As for breaking into the industry, it is very common to find graduates of that school stay on in the institutional community to work as recruiters; for example, they might have been work-study students in that very office and wanted to stay on post graduation.
However, this is certainly not to say it is the only prerequisite and you should certainly apply to jobs from schools that you did attend. Some background in education is helpful though these days more folks are coming into from private industry. In my opinion this can sometimes be a bit of a problem. Yes, a marketing background is helpful but you are not selling a car. An educational experience is something quite different and I think also having a background in education is helpful. It will allow you to better understand institutional goals and student needs. It also helps administrators have better working relationships with faculty. So if you are interested in transitioning from the corporate world into a college admissions recruiter role, or any higher education administrator role for that matter, I recommend taking a few higher education courses to get some grounding in the field.
Sometimes a master’s degree is required, though not always for a recruiting position which is pretty much an entry-level role. If you want to advance into an Assistant Director role and beyond, you typically need an advanced degree.