There are many ways to reach out to recruiters using LinkedIn. The first step is usually to check if you can spot any mutual connections on their Linkedin profile, as that can make it easier to reach out to them. You can ask your mutual connection to make an introduction, or reach out to the recruiter directly and mention them.
If you do not have mutual connections, you can reach out to ask what job openings their recruitment agency is currently working on and provide some detail on yourself, so they can see if you would be a good fit for a potential job offer.