Can I connect a mid2011 21.5 imac to a mid2012 macbook pro?

As a matter of fact, you can.

As Apple states them, here are the rules for target display mode on iMac:

click> https://support.apple.com/en-us/HT204592

Per the link above:

• Make sure that your target iMac (2011, 2012, 2013 or mid-2014) is using macOS High Sierra 10.13.6 or earlier. 

• The source Mac must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.

• The cable connecting the two Mac computers must be a Thunderbolt or Thunderbolt 2  cable.

EDIT - I will say that the setup can be problematic, so it would probably be better if you were to simply buy an inexpensive monitor for the MBP rather than use the iMac. You also would use less energy.

Yeah... a Mac is a Mac, though always ya gotta be really specific when asking for help.

In your case a Thunderbolt (or Thunderbolt 2) cable will be required.

Apple has this:

https://www.apple.com/shop/product/MD861LL/A/apple-thunderbolt-cable-20-m

It should be that simple.

And it probably is IF the Macs involved are running fully updated copies of the appropriate software, and IF the cable being used is compliant and not some cheap knockoff, and IF the Mac hardware is healthy, and IF...

A lot of users have trouble getting it to work but that's usually because they are trying to do so with the incorrect iMac and/or the incorrect version of macOS or they cheap out on the cable. I think you're in good shape with hardware and software, so don't cheap out on the Thunderbolt cable and you'll probably be just fine.

For future inquiries this may help: Writing an Effective Apple Support Communities Question - Apple Community