Oh yes! Absolutely, I teach a class full of 3 year olds to write every year with no problems.
Begin with building finger strength through threading, play dough and construction. Add in drawing and once they have some pencil control teach the letters. Teach a couple at a time, or teach them by patterns. All the round ones, all the long ones etc depending on how familiar your child is with the letters already.
We always start with learning to write their names as all kids seem to want to know that. Then mum, dad, I love you, to and from cover a lot of letters.
Beginners work well with a little lap sized whiteboard and whiteboard markers and it saves a tonne of paper while they practice