As other answers have pointed out, someone choosing not to socialise at work is not something you can, or should, do much about.
But I kinda get your feelings about it. In a team that is otherwise very chatty, having one person sitting quietly in the corner the whole time can feel off-putting. I think it's natural that you'd want to include them in the fun and to get to know them better.
Other answers have covered some options for helping your employee feel more comfortable so I wanted to add some thoughts that might help you, since you're the one asking the question.
Firstly, you need to accept that he's not very comfortable socialising in the settings you've described. Whatever the reason for it is, you can't change his personality and you don't know what's best for him.
It might be useful to remind yourself what he brings to the team. You mention that he does decent work but I'm sure he has other strengths that help the team as a whole. If talking about your personal life is an important quality in your team, it sounds like that's well covered by the other team members and perhaps someone that can remain focused on the work adds some important balance.
As a manager, I assume that your career goals have some focus on progression up the ladder. It is helpful to recognise that not everyone shares that goal and some people are content with showing up to do their job and going home again. As long as he's getting the job done satisfactorily, you don't get much say on what he should be doing in addition to his contracted responsibilities.
As your report, he might express a desire for a promotion at some point. That would be an appropriate time to suggest that better relationships with his peers would be beneficial if that would help in the new role.
If your goal is just to build a better relationship with your report, you could try talking to him about things he's interested in rather than trying to make him share personal details he's not comfortable with. This might mean talking to him about work things.