Swearing doesn’t have to result in co-worker harassment or poor public relations in order for you to send out a cease-and-desist order. If you think someone’s language is a workplace problem, that’s all the justification you need to act.
When you address the issue for the first time, approach it as a “heads up” to the worker; don’t attack, don’t discipline. Let him know what you’ve observed in terms of his behavior. Explain that the language is unprofessional and creates an unpleasant work environment that may be offensive to others.
If he needs a “what’s in it for me” incentive before making a change, explain how the constant cursing reflects poorly on him and that his language may damage his career when, say, he’s gunning for a promotion.
If the employee is not amenable to changing his ways, be prepared for a freedom-of-speech claim. Don’t fall for it! The First Amendment only applies to government employers, not private employers—and that doesn’t mean government employees are free to swear as much as they want.
Private employers do have a little more freedom to create and enforce rules and policies on workplace behavior. If the employee is being really obstinate, there is a “legal” angle with which you can approach him. Because employers are required by law to prevent harassment in the workplace, if a question ever comes down to an employee’s “right” to say whatever he/she wants versus another employee’s right to work in a harassment-free workplace, the employer’s anti-harassment efforts would win. And you don’t need to wait for another employee to complain, because you’re expected to take steps if you see or hear potential harassment with your own eyes and ears.