How to relationships field on the contact profile
The "Current Employer" field is special in that the employer_id is actually stored on the contact record (in the civicrm_contact table on the underlying database).  All other relationships are stored only in civicrm_relationship.

Nevertheless, you could fake this:


Create a custom field of type "Contact Reference".  This by itself might meet your needs - do you still need a relationship if you have a contact reference field?
If so - you can write an extension (if you're not a coder, you can hire one to do this for you) that fires on hook_civicrm_custom.  When they contact reference field is changed, a corresponding relationship can also be updated.