2011 iMac 27” Graphics Card Replacement

No. Not a user replaceable part.

I'll second the suggestion to starting by first upgrading the RAM if you haven't yet and next replacing the HDD with an SSD. That will do more to improve High Sierra performance than a new GPU.

A GPU upgrade is possible but not recommended (and would depend on which GPU you currently have... the 6970M shipped with a beefier heatsink than with the 6770M).

Physically the the 2011 iMacs used MXM laptop-style GPU cards that can be replaced, but the processes is very difficult, very complex, and very much not supported by Apple.

• You need service technician level skill (The GPU is not considered a user-replaceable part: logic board removal is required)
• You need a custom amateur/community written vbios (Apple has never made/blessed any upgrade and cards intended for windows laptop have an incompatible vbios)
• You need to be able to flash a GPU with said vbios. (Extra hardware/skill required).

You can try looking at iFixIt for some ideas and user reports of this kind of upgrade. Not totally impossible, but perhaps somewhat difficult and not very cost effective, when compared to the alternative of just buying like a newer working 2012 model, for example.

The money and time spent to do such an upgrade, if possible,

on a 9 year old computer that will likely no longer receive macOS

security updates once Big Sur is released, would be money poorly

spent.

You would be better off putting that money toward a new computer.

it's some custom PCB so you can't just get any new graphics card so it's to replace a fried one or get the slightly better one that was optional in the user config choices when you purchased it.

that being said video cards does not really make most computer operations faster, they're main speed inc is 3d and the second best are some filters for video edit.

if your computer is slow it's likely not enough system memory or the IO speed being subpar (old magnetic harddisk vs. ssd)

if you only have 4GB system memory then upgrading it would speed it up a good deal

This is what the card and its associated heat sink look like:

[image from iFixit.com]

the card part is under the metal square at the right of the image.