can we have a foreign key which is not a primary key in any other table?

Yes – you can have a foreign key that references a unique index in another table.

CREATE UNIQUE INDEX UX01_YourTable ON dbo.YourTable(SomeUniqueColumn)

ALTER TABLE dbo.YourChildTable
   ADD CONSTRAINT FK_ChildTable_Table
   FOREIGN KEY(YourFKColumn) REFERENCES dbo.YourTable(SomeUniqueColumn)