No particular emphasis is placed on a particular rocket but rather if a rocket capable of carrying a human payload exists.
The answer is either "none" or "all", depending on how you look at it.
The limiting factor is how you intend to launch the spacecraft that's actually going to carry the people to Mars.
For reference, the Apollo CSM massed about 12000 kg dry (no propellants or consumables). The CSM could keep 3 people alive for a period of a week or so; figure a spacecraft to Mars would be considerably bigger.
If you want to send the whole shebang off in a single launch (as with the Apollo missions), then you're going to need at least an SLS Block II class rocket (50,000 kg to TMI), and even then I'm not sure that's adequate (Orion is not going to be the transfer vehicle - it doesn't have the lifetime for a trip to Mars). The ITS as originally envisioned by SpaceX is insanely, stupidly huge, making the SLS look like a bottle rocket, and even then the concept requires 2 launches (one to launch the transfer vehicle, one to launch the fuel for the transfer vehicle).
Note that SpaceX is scaling back on the ITS a bit, from 12 m diameter to 9 m, which is still huge.
No commercial launcher currently in production will be able to do it.
However, if you send your transfer vehicle up as a series of smaller modules that get stacked and fueled in Earth orbit (sort of like the ISS), then pretty much any launcher is up to the task, you just have to size the individual modules appropriately. A FH (or similar class launcher) could lift the transfer spacecraft modules (along with propellant and consumables), and an F9 (or Atlas) could launch a Dragon (or a Starliner) as a taxi.
This would not be easy, but it would be more tractable than trying to do it all in a single launch.
If all you're concerned about is sending the equivalent mass of a person (or several people, say several hundred kg in total), then almost any launcher in use today can get that mass to Mars - a good chunk of the Mars exploration program was launched on an Atlas V. If your human payload doesn't have to survive the trip, you're golden.
Again, the issue isn't the people themselves, but the spacecraft required to keep them alive and healthy for months at a time in space. That's going to be your limiting factor for any human spaceflight.
Any rocket that can carry humans (NASA would say Falcon 9, Atlas V in the near future, China would say Long March 2F, ESA would say Ariane, Russia would say Soyuz) can carry them to Mars.
In reality most plans for Mars missions involve launching the transit vehicle on one booster and then the crew on another. SpaceX with ITS/BFR is actually the opposite and suggesting doing everything in one launch (well maybe multiple refueling launches of other vehicles, and then crew on a single vehicle).
So it is almost immaterial which rocket could take them to Mars, since it is really the first step of getting into orbit that matters.
Or you could have meant, does any rocket active today have the ability to launch from the surface of the earth direct to Mars.
Maybe SLS will one day, maybe Falcon Heavy, maybe ITS/BFR but nothing really available today.