How should I link these sentences?
He is a social worker. He is a teacher.
I think the correct answer is
Besides being a social worker he is also a teacher.
Assuming that the two instances of he refer to the same person, and you do not want to imply a contrast or focus on one job over the other, it's as simple as:
"He is a social worker and a teacher."
If people already know about one, but not the other (for example, in an article that introduces him as a social worker, and later introduces the fact that he is also a teacher), you might use a range of other things:
"As well as being a social worker, he is also a teacher."
"Besides being a social worker, he is also a teacher."
"He is a teacher as well as a social worker."
"He isn't just a social worker; he's a teacher as well."
There's a lot of stylistic choices to be made, but if all you want to do is deliver the two bits of information in your question, it's simplest to go with the simple 'and' sentence.
I think it should be "Besides being a teacher, he is also a social worker."
It actually depends on which profession is the full time one. I have assumed teaching as 'his' full-time profession and gave it preference over the social work job.