I have a male employee who told another employee a story about his son's sex life.  The story was very graphic.  This occured only once but it was one month ago,  I just found out about it today. 

I am new to the company and just sent out a new Sexual Harassment Policy; however, this was after this incident occured.

My question is can I terminate the employee who made the comment?  

Due to the fact that I am new to the company, I am unsure about whether he signed an employee handbook acknowledgement form.  It is not in his personnel file.  He did sign the Sexual Harrassment Acknowledgement form just this week. In addition I know that my company has not been through Sexual Harassment Training in a long time.  I know the employee who told the story has not been through training.  Can we terminate or just issue a written warning?

I wouldn't fire him if there was no written or formal policy or any training in place when he told the story.  However, the story was inappropriate, so I would give him a written warning with verbiage to state that one more occurrence may results in termination. 

He has been trained now, so anything going forward is a violation of the policy and subject to consequences.

 It's hard to retroactively enforce a policy.  It sounds like he's an employee you may want to keep an eye on though.

 Good luck!

it doesn't sound like anyone filed a complaint...i would point out your policy on sexual harassment and issue him a verbal warning - and make sure you document it and put it in his file

I agree with glasater that given the circumstances it would be difficult to terminate based on one incident, inappropriate as it was.  If the incident was reported to you as a complaint about sexual harassment then you need to investigate.  You might find out that it's not as isolated an occurrence as it appears.  And letting the storyteller know that the incident is a violation of policy is a good idea.
 

I wouldn't fire him if there was no written or formal Harassment policy or any training in place when he told the story.

rgs

Threadromancy: Noun, (1)  the dark art of bringing dead threads back to life by replying to them.

But, since it's here...

You don't have to have a policy against assault to fire someone for assaulting a co-worker.  In such common sense situations, the former employee's only real recourse is unemployment insurance.

However, you don't necessarily fire people for saying things that did not clearly offend any particular person.  It's not clear that an investigation has been conducted: how did you "just find out"?  I would issue a written warning whether anybody was offended or not.  Moreover, in the absence of any evidence that there was something else about the story, like it was being told specifically to offend or humiliate a co-worker or make them feel threatened in any way, I would not normally fire someone for a dirty mouth on a first offense in the absence of such factors or evidence that there were offended parties present.