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).