An alternative Linux/Unix - shell-escape based approach (although there is \pdfmdfivesum file {yourfilename})
It writes the hash to a file and reads it back to the original file.
\documentclass{article}
\usepackage{blindtext}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\AtBeginDocument{%
\immediate\write18{shasum \jobname.tex | awk '{print $1}'> \jobname.hash}
}
\cfoot{\input{\jobname.hash}}
\begin{document}
\blindtext[5]
\end{document}

A variation with reading to a macro:
\documentclass{article}
\usepackage{blindtext}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\newread\hashfile
\AtBeginDocument{%
\immediate\write18{shasum \jobname.tex | awk '{print $1}'> \jobname.hash}
\openin\hashfile=\jobname.hash
\read\hashfile to \filehash
\closein\hashfile
}
\cfoot{\filehash}
\begin{document}
\blindtext[5]
\end{document}