1.) First of all, can you confirm that you installed using the mricron_macOS.dmg (v1.0.20190902) available at one of these sites:
  https://www.nitrc.org/projects/mricron
  https://github.com/neurolabusc/MRIcron/releases
these should be notarized with Apple and therefore should work if you directly download them an install them.

2.) If those files do not work, have you tried installing (v1.2.20200331)?
  https://github.com/rordenlab/MRIcroGL12/releases

3.) If both options fail, does going to AppleMenu/SystemsPreferences/Security&Privacy provide an option for you to run this.

4.) If all of the above fail, can you tell me the version of MacOS you are using.