Any vegetable in moderation are supposed to be OK if you have diabetes. There are some that have a lot of natural sugars such as beetroot so eating those in moderation is probably wise. If you are on medication such as Metformin and Januvia then these should moderate any sugar intake from vegetable and fruit and there should be no particular restrictions that you need to worry about. If you are on insulin it is probably best to keep food intake to a regular routine so that you do not find yourself going out of the normal range for blood sugar.
All in all you should find no problems with eating carrots as long as you keep to a sensible amount and do not eat just carrots.
The opinions expressed here are not from a medical expert just from someone that has diabetes. This advice should not be taken as gospel and you should consult your medical team if you think you have diabetes.