There is a specific security setting for merging constituent records:
 
     
    • Open Administration and select Security
    • Open the group the user belongs to
    • In the Group Privileges list, mark the checkbox next to Administration and click the Options button
    • Mark the checkbox next to Merge Constituents
    • Click OK
    • Save and close the group record
      Note: The user must have full rights to edit all fields. If the source record will be deleted, the user must also have rights to delete constituents.