Enclosing list in a box

With standard frame, you need only add leftmargin=* option to enumerate list:

\documentclass{article}
\usepackage{enumitem}

%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}

\begin{document}
\noindent\fbox{%
  \parbox{\dimexpr\linewidth-2\fboxsep-2\fboxrule\relax}{
  \begin{enumerate}[label=Step \Roman*, leftmargin=*]
    \item   item 1
    \item   item 2
    \item   item 3
    \item   item 4
    \item   item 5
    \item   item 6
    \end{enumerate}
                    }%
        }
\end{document}

(red lines indicate page layout)

If you want to put frames etc round your list environment then I suggest using tcolorbox as this will give you much more control. For example, you can produce

using the code:

\documentclass{article}
\usepackage{enumitem}
\usepackage{tcolorbox}

\newlist{steps}{enumerate}{1}% create new steps environment
\setlist[steps]{%              configure the steps environment
  label=Step \Roman*,
  leftmargin=*,
  align=left
}
\tcbuselibrary{skins}
\tcolorboxenvironment{steps}{% wrap the steps environment in a tcolorbox
  colframe=red!75!black
}

\begin{document}

  \begin{steps}
    \item item 1
    \item item 2
    \item item 3
    \item item 4
    \item item 5
    \item item 6
  \end{steps}

\end{document}

A few comments about the code:

• The MWE example appears to be using the enumitem package so, as above, I recommending using \newlist to define a custom steps environment and then \setlist to configure this enivorment.
• The \tcolorboxenvironment{steps}{...} command wraps the steps environment inside a very simple tcolorbox, which is highly customisable. I recommend reading the tcolorbox manual, after which you can configure this to your heart's content.