documentclass{beamer}
usetheme{CambridgeUS}
begin{document}
begin{frame}{Centering the itemize}
  My first try: Centering the itemize
  begin{center}
    begin{itemize}
      item item1
      item item2
    end{itemize}
  end{center}

  begin{center}
  My second try: Centering the itemize
  begin{itemize}
    centering
    item item1
    item item2
  end{itemize}
  end{center}
end{frame}
end{document}

documentclass{beamer}
usetheme{CambridgeUS}
newcommand{tabitem}{%
  usebeamertemplate{itemize item}hspace*{labelsep}}

begin{document}

begin{frame}{Centering the itemize}
  My first try: Centering the itemize
  begin{itemize}
    item item1
    item item2
  end{itemize}

  begin{center}
    begin{tabular}{@{}l@{}}
      My second try: Centering the itemize \
      tabitem item1 \
      tabitem item2
    end{tabular}
  end{center}
end{frame}

end{document}