Is there a taxi turning radius requirement for normal category aircraft?
There is no legal requirement. In fact there is no stipulation that the aircraft be maneuverable on the ground. 

Good examples of this are early aircraft (often biplanes) with tail skids. In the middle part of the last century there where gliders that had no wheels - just a center skid. Many current gliders have just one wheel and it is not steerable. 

"The nose gear of a few aircraft with tricycle-type landing 
gear is not controllable." FAA Airframe Handbook pg 13-4

These type of aircraft are usually steered using differential braking. Examples are: Grumman (AA1, AA5, AG5), Diamond (DA1, DA4), Rallye except the 235C, early "straight 35" Bonanza, Columbias, T-28, T-34C, Nanchang CJ-6A, HU-16 Albatross, IAR 823, etc.  



The HU-16 Albatross does not have steerable gear



Aircraft without wheels



Glider without steerable gear