To do that, you would need to install an app on your phone which can listen to requests for information from your computer. And you would need to grant that app permission to view your browsing history. (Like how apps request permission to access your location data.) The bad news is, as far as I can tell, iOS doesn't even have a way for apps to request permission to view the browsing history.

If you want to be able to, say, keep a log of your phone's browsing history, a better option might be to install an HTTP proxy on your computer, and configure the browser on your phone to route all requests via that proxy. Given how much of the web uses HTTPS now, this is probably of limited value though.