From the questions wording you mean, could we lift the Apollo CM/LM stack on any existing boosters? In that case no. Largest heavy lift vehicle is probably Delta-4-Heavy. Falcon Heavy is not yet operational and will exceed it, but has a low Isp upper stage so is not optimal for such missions.
Could a different moon mission be launched? Almost certainly, just a matter of launching in smaller pieces and likely refueling in orbit. Would it be worth it? Well clearly no one has thought it worthwhile to date.
You would launch something like the Command Module and Service module (In one or two modules), where the Service module would act as an upper stage, and then refuel it in orbit from following launches. Then another launch for a Lunar Module, assemble in orbit and onwards.
There is a lot of speculation that the Falcon Heavy demo payload might be an Apollo 8 style mission, where a capsule is sent to go around the moon and come back.
If there was a true desire to do so, it is likely possible, but no one has decided it is necessary.
Additionally, consider costs. A Saturn V in modern dollars has been estimated in \$2 billion dollar range a launch. A Delta 4 Heavy is around \$400 million a launch. A Falcon Heavy launch is advertised at \$125 million. (Assuming they ever develop cross feed). Thus even 5 Delta 4 Heavy launches is competitive with a Saturn V, and as many as 16 Falcon Heavy launches.
With the experience of building the ISS a lot of technology and tools for in space assembly has become much more feasible than in the 1960s on a tight deadline.
We probably no longer need a giant super booster just for the moon, even though SpaceX plans to build one as the BFR/MCT combo for Mars missions.