Can I upgrade CPU to i7 4770k for my 2013 27" iMac?

The K CPU series doesn’t work in this iMac - it’s not coded in the EFI firmware as supported.

The problem with finding a 4771 is that CPU is made just for Apple and even Apple doesn’t supply it as a spare part separately. The only way Apple supplies it is as a part of a motherboard assembly, and it is covered with tamper evident seals. Unless it’s pulled from a Mac and sold as used, the CPU is probably fake.

The other issue is this is a high risk upgrade, often with so little performance gain even the people who get it right second guess why they bothered.

Most people are usually going from a very capable i5, to an i7. The performance gain is usually minor compared to a SSD and RAM upgrade. These are nowhere near as difficult to install.

The problem with these “thin” iMacs is most first time DIYers ruin the LCD by using the wrong tools (and technique), and then dropping the screen so you need to replace the LCD cable AND screen ($$) and repair or replace the motherboard ($$$). Refer to this guide for steps: iMac Intel 27" EMC 2639 CPU Replacement. Before you do this, compare your current CPU and the i7 4771 and see if the risk is worth it. For most people, it isn’t.

I could handle this job if I got a deal on one, but even I would probably pass because of the work required vs. the performance gain! Refer to this link to see how much of a difference the 4771 would make. It’s not worth it.