How can I create a Foreign Key to a Compound Primary Key with a single column?
Yes, you can do this with a COMPUTED column, It's a workaround really as the column has to be PERSISTED to be used for the foreign key constraint so it consumes storage space:

CREATE TABLE dbo.OtherTable (
    ID INT PRIMARY KEY IDENTITY(1,1),
    Blah VARCHAR(100),
    FieldName AS CAST('This' AS VARCHAR(100)) PERSISTED NOT NULL
) ;

ALTER TABLE dbo.OtherTable WITH CHECK 
  ADD CONSTRAINT [FK__OtherTable__Blah] 
    FOREIGN KEY (FieldName, Blah) 
    REFERENCES Lookup (FieldName, Value) ;


Tested at SQL-Fiddle.

The table can then be used as if the FieldName does not exist. You could even define a view that does not include this column and make your applications use that view: SQL-Fiddle-2



The syntax you hoped for, although looking pretty, has not been implemented in any DBMS I know of:

ALTER TABLE dbo.OtherTable WITH CHECK 
  ADD CONSTRAINT [FK__OtherTable__Blah] 
    FOREIGN KEY('This', Blah) 
    REFERENCES Lookup (FieldName, Value) ;


Note however that the workaround with the computed columns would be 100% equivalent to this syntax, if only SQL-Server removed in the future the restriction of using only persisted columns. You could add a Connect item with your request.

For the question whether there is any other DBMS that allows this, no, there isn't. Check also a related question:  

Are there DBMS that allow a Foreign Key that References a View (and not only base tables)?



If you really don't want to  use this method (because of the additional storage requirements, alternative paths would be to enforce the constraint via procedures or triggers (Note that you would have to write procedures or triggers for both tables involved.)