Yes, you can swap a Joker in Mahjong Island. On your turn, you may trade a real tile from your Rack for a Joker in any Open Group. The Joker must stand for the tile you give. Then the Joker is yours to use in your own hand.
A few words first. Your Rack is where your own tiles sit. A Group is a few identical tiles, like a Set, three matching tiles. An Open Group is one a player has already laid face up on the table.
What does a Joker swap look like?
A swap replaces the Joker with the real tile it stands for. Say another player shows the Set below. It has two 5 Crak tiles and a Joker standing in for the third.
If you hold a real 5 Crak, you can make the swap on your turn. Place your 5 Crak in their Set. Take the Joker back to your Rack. Their Set is still complete, now with three real tiles.
Why is a Joker worth taking?
A Joker is wild, so it can help many hands. It can stand in for a tile in a Set, Quad, Quint, or Sextet. It cannot fill a Single or a Pair, which is two identical tiles.
Every game deals 8 Jokers, each a different kind. A Joker scores the Chips of the tile it stands for. Each kind also adds its own Mult, a multiplier on your score. The guide to Jokers and Bonus Hands explains each kind.
When can you not take a Joker?
You cannot take a Joker from the discards. A discarded Joker is dead, so nobody can take it. Jokers are also never passed in the Charleston. Read more in Can You Discard a Joker in Mahjong Island?.
Your goal stays the same with or without a swap. You win by completing one hand on the Island Card: 14 tiles that match one line. The Mahjong Island rules guide walks through a full hand.