Should I refrain from giving oral sex if I have a canker sore in my mouth?

Play it safe. Apthous-type ulcers are more benign but the previous answer provides warning about the spread of a virally produced lesion. Be safe...Since you dont know which you are dealing with, refrain.
Yes. Yes, any sore in the mouth is a perfect avenue to transmit an std. The activity of oral sex could also aggravate the ulcer.
Canker Sore is Ulcer. A canker sore is also known as an aphthous ulcer. Since an ulcer is a break in the mucous membrane that is a barrier for invasion from bacteria, yeast and virus, it would seem advisable to reframe from oral activities that might lead to picking up an infection.