Can a ringtone I purchased be captured on my sim card?
No. The only thing that can be saved onto a sim card are contacts.
Really? I have photos and music and contacts, oh my!
I’ve never downloaded a ringtone, though, and just use my own music.
Those things may be stored on your phones internal memory or storage card, but they are not stored on the SIM card. If you transfer your SIM to a new phone, only the contacts and some SMS messages go across (if you have copied your contacts to the SIM card, and the SIM contact format is usually a subset of what your phone contact supports).
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If you’re simply looking to get the ringtone back, call your cell provider and they should send it to you, free of charge, assuming you’ve already paid for it once. (This may not be related to your question at all…if so, disregard.) 