Just to clear a few things: I don't think there is anything that can tell this, not only in Joomla but in anything in the web. Under certain conditions you may be able to tell if a certain browser was at your site recently, e.g. like what G. Analytics does when counting new vs old visitors, which is a cookie based solution.
But there is no real accuracy on such metrics, so if you are trying to implement specific critical things based on that, simply you can't.
So with this in mind you need to clarify and narrow down or change your requirements on what you are trying to do, based on what is actually feasible.
Update for your comment:
I don't know exactly how Google handles it, but briefly from what I have read on the subject, the GAnalytics JS sets a cookie on the user's browser and assigns a unique id for that user which is also stored on Google's server. So in case this user returns, GA JS reads the cookie and knows that this user is a returning one.
I don't know for sure, but I am almost certain that there is nothing like that is provided by Joomla - and frankly I don't think Joomla needs to provide something like this.
But depending on what you are actually want to do, this can be as simple as setting a cookie in the user's browser.