Align minipage on right side

I, in fact, would use a tabular environment for the title and the text; for the text, a p{<length>} column (and @{} to remove the extra space); inside the tabular, the title can be centered using \multicolumn:

\documentclass{scrartcl}
\usepackage{showframe}
\usepackage{lipsum}

\begin{document}


\hfill\begin{tabular}{@{}p{.5\linewidth}@{}}
\multicolumn{1}{@{}c@{}}{Some title} \\
\lipsum[4]
\end{tabular}

\end{document}

If this structure will be used several times, an environment can be defined; in the following example, the newly defined myenv environment has one mandatory argument (the title) and an optional argument (the width used to typeset the text with a default value of 0.5\linewidth):

\documentclass{scrartcl}
\usepackage{showframe}
\usepackage{lipsum}

\newenvironment{myenv}[2][.5\linewidth]
  {\par\hfill\tabular{@{}p{#1}@{}}
  \multicolumn{1}{@{}c@{}}{#2} \\ }
  {\endtabular\par}

\begin{document}

\begin{myenv}{Some title}
\lipsum*[4]
\end{myenv}

\begin{myenv}[.8\linewidth]{Some title}
\lipsum*[4]
\end{myenv}

\end{document}

If the title spans more than one line, one could load the array package in the preamble:

\usepackage{array}

and then say

\newenvironment{myenv}[2][.5\linewidth]
  {\par\hfill\tabular{@{}p{#1}@{}}
  \multicolumn{1}{@{}>{\centering}p{#1}@{}}{#2} \\ }
  {\endtabular\par}

You can use 100% plain LaTeX with boxes and the minipage environment:

with showframe:

without showframe (see example):

Example:

\documentclass{scrartcl}
\usepackage{lipsum}

\begin{document}
\noindent% prevent the box to be shifted a bit to the right
\makebox[\textwidth][r]{% create a box, with it's content aligned to the right
  \begin{minipage}{.5\textwidth}% create a content half width
    \section{Some title}
    \lipsum[4]
  \end{minipage}
}
\end{document}