You can do this using the
INDIRECT function. Suppose we want formulas in cells B1, C1, D1... that should reference A2, A3, A4... Starting in cell B2 we can enter:
=INDIRECT("R[" & COLUMN(RC)-1 & "]C1", FALSE)
In cell B2, this will render as:
In this situation, I'm using R1C1 format. The second parameter to the
INDIRECT function tells the function to use R1C1 format. The function itself (again in cell B2), says "give me what is in the cell that is one row down and the first column". In the original formula, by basing the row value on the current column number, it will update the formula to a new row as you fill right.
Now, if you are asking if there is a way to do this using the GUI like say using the Fill box with the mouse, the answer is no. There is no means to transpose the fill using the GUI.