Yes, CAME is a Scrabble word!

verb

1. move toward, travel toward something or somebody or approach something or somebody
2. reach a destination; arrive by movement or progress
3. come to pass; arrive, as in due course
4. reach or enter a state, relation, condition, use, or position
5. to be the product or result
6. be found or available; The furniture comes unassembled"
7. come forth
8. be a native of
9. extend or reach
10. exist or occur in a certain point in a series
11. cover a certain distance
12. come under, be classified or included
13. happen as a result
14. add up in number or quantity
15. develop into
16. be received
17. come to one's mind; suggest itself
18. come from; be connected by a relationship of blood, for example
19. proceed or get along
20. experience orgasm
21. have a certain priority