Yes, gotten is a Scrabble word!

Verb

1. Come into the possession of something concrete or abstract
2. Enter or assume a certain state or condition
3. Cause to move; cause to be in a certain position or condition
4. Receive a specified treatment (abstract)
5. Reach a destination; arrive by movement or progress
6. Go or come after and bring or take back
7. Go through (mental or physical states or experiences)
8. Take vengeance on or get even
9. Achieve a point or goal
10. Cause to do; cause to act in a specified manner
11. Succeed in catching or seizing, especially after a chase
12. Come to have or undergo a change of (physical features and attributes)
13. Be stricken by an illness, fall victim to an illness
14. Communicate with a place or person; establish communication with, as if by telephone
15. Give certain properties to something
16. Move into a desired direction of discourse
17. Grasp with the mind or develop an understanding of
18. Attract and fix
19. Reach with a blow or hit in a particular spot
20. Reach by calculation
21. Acquire as a result of some effort or action
22. Purchase
23. Perceive by hearing
24. Suffer from the receipt of
25. Receive as a retribution or punishment
26. Leave immediately; used usually in the imperative form
27. Reach and board
28. Irritate
29. Evoke an emotional response
30. Apprehend and reproduce accurately
31. Earn or achieve a base by being walked by the pitcher
32. Overcome or destroy
33. Be a mystery or bewildering to
34. Take the first step or steps in carrying out an action
35. Undergo (as of injuries and illnesses)
36. Make children