This is totally acceptable and very clever if you want to get your foot in the door at a company that’s hard to get into.
Check out a company’s social media accounts to do background research, and follow the senior officials there. You don’t have to connect with every senior official. You can simply start by connecting with people who you admire through outlets like LinkedIn and Twitter.
Follow them and be sure to like and re-tweet what they write.
Only do this if you have a clean social media presence, otherwise you could risk turning them off.