The word for family in Japanese is 家族 (kazoku), so it would be best and safest choice to inscribe in your ring.
If you are specifically looking for a single character instead of two, then it gets trickier. In such case I would still recommend the single kanji 家 (which is again contained in 家族). 家 means house or home, but it can also mean family, used as a suffix (i.e. the Potters would be Potter家). However, if you need only one kanji, I would ask for more advice because I'm not completely sure it's the best choice.
If 2 kanji are ok, then 家族 is definitely why you are looking for because it's the direct and obvious translation from "family"
definitely what*
Family
Hello everyone! I want to get a ring with the symbol for "family" on it. I just don't want to be disrespectful to the language or end up with people who get tattoos of "cabbage" b/c they thought it meant "wisdom". So if I put this on the ring, will it be properly express the concept of family? 氏
I hope this question makes sense!