Hello Aspirant, Hope you are doing good.

Yes ,arts student can get admission in food and nutrition .
but it will be difficult for an arts student with Science subject but there's a way out. You can go for a certification program in dietician and nutrition which is for six months. Then you can pursue BSC in dietician and nutrition.

Diploma in Food and Nutrition is 1-3 year Diploma program which focuses on detailed knowledge of food preparation and selection of nutritional supplements in diet. Candidates must have passed Class 10+2 or equivalent in relevant discipline from a recognized board with an aggregate mark of 55%.
For more information can visit the link given below.

https://www.careers360.com/courses/diploma-in-dietetics-and-nutrition

Hope this information helps you.
All the best.