Private companies can require that you not smoke at work or even away from work. With that, there will be companies that require employees to take a vaccine as a condition of hiring and employment.
Not unless they have drastically changed the rules. They can require that you not smoke in the building but they can not require that you not smoke on your breaks in other areas.
The only way they can require you not smoke away from work is if you have signed something to get a cut on your medical insurance. In that way they have essentially paid you not to smoke.
Even that is legally iffy.