Any future society capable of devising the technology required to time travel into the past is not going to bother with anything as quaint as a cell phone. There are sufficiently capable in-ear devices in use even today that are capable of audio based communication and are much less conspicuous than holding a box to your head. Are we to think that we'll still be slugging around cell phones in our distant future, when sci-fi writers would have us believe that in-eye HUDs will be supplementing our realities? What is the point of toting around technology, when its built right into us?
Now, I know what you're thinking: BUT Doctor Who replaces the SIM card for each of his companions so they have a time-travelling cell phone. Yes, that's right, but its also because that's what that person's time is comfortable using. Heck, the form of the TARDIS itself is a throwback to this same idea. It was a comfortable icon at the time the series was actually created.
Now, yes, maybe this time traveler is "lost" and is improvising a makeshift communicator with readily available materials. I mean, that's what Data would do.