It is not straightforward to access the clipboard contents but one way, that doesn't involve writing and reading from temporary notebooks is to use the undocumented [`ClipboardNotebook`][1] function:

    CellPrint /@ StringSplit[NotebookGet[ClipboardNotebook[]][[1, 1, 1]], "\n"];

See also this [answer][2] which mentions some caveats.  This prints strings as text cells.  See the documentation for [`CellPrint`](http://reference.wolfram.com/mathematica/ref/CellPrint.html) if you require another form.


  [1]: https://mathematica.stackexchange.com/questions/805/what-are-some-useful-undocumented-mathematica-functions/807#807
  [2]: https://mathematica.stackexchange.com/a/58623/5414