Absolutely!
You can drink celery juice everyday, in fact, there are a whole host of health benefits associated with regular consumption of celery juice.
A glass a day will help your body with digestion, anxiety, and blood pressure to give a few examples.
This is based on drinking around 16oz of celery juice daily while on an empty stomach.
The best thing to try is drinking smaller amounts of celery juice in the beginning, and then gradually increasing the quantity up to 16oz if you notice no ill effects.