Edit :
I think you mean to say that you're decreasing the initial concentration by diluting. The reasoning would be different :
HA <----> H+ + A-
t=0 Co 0 0
t<> Co-x x x
Note that here I assumed the conc of H+ is approximately 0 M and that the acid is a monoprotic weak acid.
Let's assume Co - x = Co
Then at Eq : Ka = x2 / Co
If we dilute the solution by a factor of 10 for instance:
Conew = Co / 10
xnew = x / 10
Q = xnew2 / Conew
Q = x2 / 10Co = Ka / 10
The rxn in this case must shift further to the right, and the degree of ionization increases according to Le Chatlier's principle.
P.S. IF you decrease the conc Co by lowering the quanity of the acid ( which I assumed 1st ) , the rxn shifts backward and degree of dissociation ( wrt to the ions ) would increase.