Can I use my iMac 27” (2010) as a monitor for my MacBook Pro?

Please read Use your iMac as a display with target display mode - Apple Support And it will tell you if the MBP can use the 27” iMac or not. As you were not specific about the version of Mac OS the MBP is running this is the best we can offer. To be honest TDM has been dead for many years so the chances are not good that it will work for you.

If you find it will not then I strongly recommend getting an external display for the MBP, this is far easier to setup and run as well as being more reliable than Target Display Mode ever was.

Best of luck.

Your 2010 iMac originally ran a version of Mac OS X 10.6 (Snow Leopard). You can't upgrade it past macOS 10.13.* (High Sierra). High Sierra is seven major versions behind Sequoia (the current version of macOS). Even developers who have a history of supporting old versions of macOS have abandoned it.

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The Target Specifications for your iMac say that it accepts DIsplayPort input.

iMac (27-inch, Mid 2010) - Technical Specifications - Apple Support

If that's all there was to it, you would just need a $20 USB-C to Mini DisplayPort adapter cable (and knowing how to turn on Target Display Mode) and you would be in business. (The Thunderbolt connecting hardware needed for the 2011 - mid 2014 iMacs is more exotic and MUCH more expensive.)

However, Apple retroactively added restrictions on the DisplayPort video source: it now must be a Mac released in 2019 or earlier, running Catalina or earlier. All current Macs are too new to qualify.

I am going to throw this out here. It's a thread from a couple weeks ago where one user reports they have a Mac mini M4 connected to an iMac (2009) DisplayPort input using a USB-C to DisplayPort cable.

Is there a switch or toggle for a Mini-Di… - Apple Community

Take it with a grain of salt because this is an outlier. We haven't seen many (any?) other reports of this.