From a post by Douglas Steele, ACCESS MVP:
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Take a look at http://support.microsoft.com/?id=138909

Once you've saved all that code into a new module (make sure you don't name
the module ClipBoard_SetData!), you'd simply need to put
ClipBoard_SetData(strNumbers) in your code somewhere.

http://support.microsoft.com/?id=138910 shows similar code for reading from
the clipboard.
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You then could run code via button click event that would use the
ClipBoard_SetData procedure to read the .Value of the textbox and write it
to the clipboard.