SQL - Call Stored Procedure for each record

I am looking for a way to call a stored procedure for each record of a select statement.

SELECT @SomeIds = (
    SELECT spro.Id 
    FROM SomeTable as spro
    INNER JOIN [Address] addr ON addr.Id = spro.Id 
    INNER JOIN City cty ON cty.CityId = addr.CityId
    WHERE cty.CityId = @CityId
)


WHILE @SomeIds  IS NOT NULL
BEGIN
    EXEC UpdateComputedFullText @SomeIds
END

Such a thing above is not working of course, but is there a way to do something like that?

You need to use a cursor for that.

DECLARE @oneid int -- or the appropriate type

DECLARE the_cursor CURSOR FAST_FORWARD
FOR SELECT spro.Id  
    FROM SomeTable as spro 
        INNER JOIN [Address] addr ON addr.Id = spro.Id  
        INNER JOIN City cty ON cty.CityId = addr.CityId 
    WHERE cty.CityId = @CityId

OPEN the_cursor
FETCH NEXT FROM the_cursor INTO @oneid

WHILE @@FETCH_STATUS = 0
BEGIN
    EXEC UpdateComputedFullText @oneid

    FETCH NEXT FROM the_cursor INTO @oneid
END

CLOSE the_cursor
DEALLOCATE the_cursor

Put the Ids into a Temporary table variable, and then iterate throught each row: (You do not need to use a cursor which will be considerably slower)

   Declare @Keys Table (key integer Primary Key Not Null)
   Insert @Keys(key)
   SELECT spro.Id  
   FROM SomeTable as spro 
       JOIN [Address] addr ON addr.Id = spro.Id  
       JOIN City cty ON cty.CityId = addr.CityId 
   WHERE cty.CityId = @CityId
   -- -------------------------------------------
   Declare @Key Integer
   While Exists (Select * From @Keys)
     Begin
         Select @Key = Max(Key) From @Keys
         EXEC UpdateComputedFullText @Key
         Delete @Keys Where Key = @Key
     End 

EDIT Delete is not slow when used with a filter predicate driven against a very narrow unique index, as this is. But it can easily be avoided, just by making loop as follows:

Declare @Key Integer = 0
While Exists (Select * From @Keys
              Where key > @Key)
 Begin
     Select @Key = Min(Key) From @Keys
                   Where key > @Key
     EXEC UpdateComputedFullText @Key
     -- Delete @Keys Where Key = @Key No Longer necessary 
 End