Throughout the film (and novelization), Jyn never demonstrates any Force powers. She doesn’t seem to be using any overt powers, such as mind tricks or telekinesis, but she also doesn’t exhibit the more mundane abilities common to Force-sensitives, such as uncanny aiming skills or piloting ability. Sure, she can take out a few stormtroopers, but that’s in line with what we’ve seen from other Star Wars characters highly trained in combat, such as Han Solo or Jango Fett.
This is generally consistent with the general vision for the film. As mentioned by a Rogue One screenwriter:
For a long time in the story, there were Jedi around, even if only in
the background. Jyn’s mother was a Jedi. But we thought that it would
be more interesting to have a story without Force powers, without
lightsabers. We could explore a period of broken faith, a galaxy
(Of course, given that Chirrut is probably Force-sensitive, they may not actually have done this….)
As for "becoming one with the Force," that’s something that anyone can do. It’s retaining one’s consciousness and ability to interact with the world to some extent (as a Force ghost) that takes skill and training.
That said, we can’t rule out the possibility that she has some (low) level of Force-sensitivity. Force sensitivity is not all or nothing: talents with the Force range from imperceptible to over 20,000. Further, her mother Lyra claimed to be able to feel the Force.
She had lost the weight she’d gained with Jyn, but was getting soft
after all the months of waiting around for the situation to change. In
the months before she and Galen had departed for Vallt, she would
often sky-cab to the Jedi Temple grounds and exercise there, basking
in the energy of that elegant site, surrounded by a nexus of the
Catalyst: A Rogue One Novel
While this might be mere religious belief, there could be something more to it. And if Lyra is Force-sensitive, it’s possible that Jyn is as well. Nonetheless, since heritability of the Force is unreliable, we shouldn’t place too much confidence in this.