It depends.
If your son is under the age of 24 and a full time student and he didn't pay more than half of his own support - you can claim him regardless of how much he made.
If your son is 24, his gross income must be less than $4,050 and you must pay more than half of his support in order to be able to claim him. It doesn't really matter how long your son worked, it matters how much he made...