I was reading a thread earlier where people who are hiring recent college grads said that they look at the applicants social media accounts and google them before they hire them. I don’t have any social media accounts just because, personally, I think they’re a waste of time. Would this be a red flag to a potential employer if they google my name and don’t find anything? Would an employer find it odd that I don’t use social media, think I’m anti-social, etc.? I would prefer responses from people who actually hire.
The only red flag would be if someone else had the same or similar name that you have, his/her social media account came up, and it contained something that is a turn-off to the employer.
I may have written one of the posts you read. 
I would probably be a bit surprised not to find any social media for someone your age but it wouldn’t worry me. Some people just aren’t into social media or are very conservative about what they put on the net. OTOH, just about everyone has some kind of digital footprint, so when I google someone I pretty much know I’ll get something. What I’m looking for is for the first few hits to be for things like HS soccer rosters, hometown newspaper stories about community service, listings for college leadership positions in clubs or the like. What I don’t want to find are obscenity-filled tweets, police reports, sexist jokes posted on FB, drunken vines or membership in groups I think are dangerous or antithetical to the position I’m hiring for.
The only exception would be if the position called for a lot of social media savviness. If the job was to grow my organization’s Facebook presence or build a Twitter following I might decide you weren’t the best fit for the job.
Try googling yourself to see what comes up and do an image search as well.
Adding in response to @ucbalumnus’s post, if I’m not 100% sure I have the right person I simply look a little deeper into the account. Unless a FB account is on total lock-down you can see most people’s friends lists and by looking at the friends’ pages you can see if they go to the same college or are from the same town as the person you’re checking on.
I share my name with a few notable people, so when someone looks me up on Google, they find a lot of irrelevant information. It’s never been an issue. Realistically, social media is used mostly as a weed-out function, to see if you have lied on your resume or done something that could cause problems for the company (if you apply to the NSA, you should probably not have something on Facebook praising Snowden…that sort of thing)… I haven’t heard much about social media being used to add to the overall package. In other words, a lack of social media won’t hurt.
Plenty of people deliberately eliminate their social media footprint while on a job hunt. It isn’t too big a deal.