No, a Joker cannot be used in a Pair in Mahjong Island. A Pair is 2 identical tiles, and both must be real tiles. A Joker can never stand in for either one.
So if a hand on the Island Card asks for a Pair of Red Dragons, you need two real Red Dragons. A Red Dragon and a Joker will not count.
Where can a Joker go instead?
A Group is a batch of identical tiles in a hand on the card. A Joker is wild only in a Group of 3 or more: a Set, Quad, Quint, or Sextet.
Why does this matter when you play?
Every Mahjong Island game deals 8 Jokers. They help you finish Sets and Quads. Any Pair in your hand still has to come from real tiles on your Rack, the row of tiles in front of you. When you hold a Joker, save it for a Set, Quad, Quint, or Sextet.
To learn which tiles can make a Pair, read can a Pair be any tile in Mahjong Island. For every Joker rule in one place, see the Mahjong Island Jokers guide.