Add relationship on profile submission
There is a scenario where a relationship can be created via a profile. If you add a "Current Employer" field to a profile, the employer gets created or matched by name and an "Employee of" relationship is created between the individual and the employer.

If you need more flexibility, the CiviRelate extension may help.

If this doesn't meet you needs, I would consider using the Webform CiviCRM Integration module, if that's feasible in your case.