When a potential employee applies for a job they are hoping to present themselves in the best light possible. They are in charge of their own CV and behavior during an interview. However, if they will be hired to have a public role representing your company, you're well within your rights to do a deeper investigation into their online presence.
The thing about social media is that it's out there for the public to see. When it comes to tweets, comments and other types of public postings that job candidate can't expect those to remain secret. If you want to find out more about a prospective employee you can start with their profile picture.
Search By Image
A person who posts a profile will often use the same profile picture. You can find out where all those pictures have been used by installing Google Chrome. There is a easy to use extension plug-in called "Search by Image." You'll need to ad that app to your Chrome and you'll be good to go.
Once it is installed, all you need to do is right click the photo and use the "Search Google with this image" option. You should be directed to a page of duplicate photos. Each one of those photos can link to a different social media account where that profile picture was used. You'll be able to follow that person onto Twitter, LinkedIn or Facebook. If they have a blog or YouTube Channel you can also find a pathway to those accounts with the Google Image Search.
Keep in mind that this isn't an invasion of privacy. If someone posts pictures of themselves going wild at a bachelor party or hurling slurs in a comment section then they are being their own worst enemy. Just because you can post something doesn't mean you have to post everything! A person's discretion with their public profile says a lot about their character.
Expanding Your Search
Once you've found links to their social media accounts you can get a sense of how they interact in various forums. You can use this same tool to track information about your own company. If you have a product picture on your website that might have been snagged by someone to post in their own blog. Do they have permission for that? Are they saying disparaging things about your brand? If you discover something like that hopefully you can bring a quick end to the negativity.