Case when you are working with initSID.ora file:

1. Change the new paths in the init parameter CONTROL_FILES - Reference
2. Shutdown the database in a clean way ( Preferrable overall is this a production database
3. Move with OS commands the control files to its new location.
4. Startup the database

Case when you are working with spfileSID.ora file:

1. Change the new paths of the CONTROL_FILES parameter in the spfile with
   ALTER SYSTEM SET CONTROL_FILES=... scope=SPFILE\"
   CONTROL_FILES - Reference
   ALTER SYSTEM - Reference
2. Shutdown the database in a clean way ( Preferrable overall is this a production database )
3. Startup the database