Yes, it is possible to repair laptop charger. It depends on problem. It is possible to change the wire with the power male jack, replace capacitors, if they cause the problem and so on. But it is better to buy new, because they are quite cheap on the Internet shops. And I am not sure if you find the repair cost reasonable, comparing to new charger cost.
By the way, the problem may be inside your computer, not in charger. If so, the repair also is possible.