Joindre means to connect two entities, to make them touch/communicate/act together.

Joindre les deux bouts. To make end meet.

Joindre l’utile à l’agréable. To mix business with pleasure.

Rejoindre means either to reconnect things that were disconnected before or to move toward and reach someone/something.

The meaning is sometimes equivalent:

Venez nous rejoindre ! Come and join us!

Venez vous joindre à nous ! Come and join us!

but sometimes, it is clearly different. Compare:

Je n’ai pas réussi à le joindre : I was unable to reach him (because he didn’t pick up the phone).

Je n’ai pas réussi à le rejoindre : I was unable to reach him (because I was too slow).