The plug to the socket is broken

Khalid, if it's just the plug that's broken, you can buy a replacement at a hardware store. You would then cut the old plug off the end of the cord and attach the replacement plug. Here's an example of the kind of thing you'd need.

Leviton 15 Amp 125-Volt 2-Pole 2-Wire Polarized Plug, White 101-WH R62-00101-0WH - The Home Depot

If, on the other hand, it's the cord that's the problem, then you have two choices. If the damaged part is near the plug, you can cut that part off and just put on a replacement plug like the one above. That will leave you with a shorter cord, and hopefully it'll still be long enough to use. Otherwise, you should buy a length of cord with a plug already molded on, and replace the entire cord. That is, of course, more work as you have to take the fan apart to be able to get to the end of the cord inside. Here's an example of the sort of cord I'm thinking of.

GE 8 ft. Replacement Cord Set with Polarized Plug on 1-End, Black 54435 - The Home Depot

Cords come in different lengths and colors, so pick one that suits you. As I mentioned, replacing the whole cord is a bit more complicated, but this teardown guide should give you the information you need to get to it.

Holmes 16 Inch 4-in-1 Fan Teardown - iFixit

I can't be sure, but it looks like the cord is simply attached with wire nuts, so you should just be able to unscrew them, separate the wires, twist together the new wires and reattach the wire nuts. Of course you'll need to thread the cord through the existing openings and it looks like theres's a protective plastic sleeve you'll want to transfer over, but otherwise a little common sense should get you through it.

If you have time, take lots of pictures as you work and once you're done you can use them to create your own iFixit guide to that repair. It's easy, fun and will earn you the appreciation of the repair community.

Create a new Guide - iFixit