Q: How do you authorize a new computer in icloud?

Authorization and Deauthorization

See iTunes Store- About authorization and deauthorization for Macs.

See How to Authorize or Deauthorize iTunes | PCWorld for Windows.

In iTunes you use the Authorize This Computer or De-authorize This Computer option under the Store menu in iTunes' menubar. For Windows use the ALT-S keys to access it.

More On De-authorizing Computers (contributed by user John Galt)

You can de-authorize individual computers, but only by using those computers. The only other option is to "de-authorize all" from your iTunes account.

  1. Open iTunes on a computer

  2. From the Store menu, select "View my Account..."

  3. Sign in with your Apple ID and password.

  4. Under "Computer Authorizations" select "De-authorize All".

  5. Authorize each computer you still have, as you may require.

You may only do this once per year.

After you "de-authorize all" your authorized computers, re-authorize each one as required.

If you have de-authorized all computers and need to do it again, but your year has not elapsed, then contact: Apple - Support - iTunes - Contact Us.

Choose Authorize Computer from the Store menu at the very top of the computer's screen.

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That will authorize my Mac for playing iTunes content, but it will not authorize it for iTunes in the cloud, which I believe the questtion was for.