Since KOMA-Script version 3.20 there are options to change the style of the TOC or list entries. You can use
\RedeclareSectionCommands[tocdynnumwidth]{chapter,section}
to get

or
\RedeclareSectionCommand[tocnumwidth=2.3em]{chapter}
\RedeclareSectionCommand[tocindent=2.3em,tocnumwidth=3.2em]{section}

Code:
\documentclass{scrreprt}[2016/05/10]% needs version 3.20 or newer
\RedeclareSectionCommand[tocnumwidth=2.3em]{chapter}
\RedeclareSectionCommand[tocindent=2.3em,tocnumwidth=3.2em]{section}
\renewcommand*\thechapter{\Roman{chapter}}
\begin{document}
\tableofcontents
\setcounter{chapter}{6} % Problem starts at chapter 7
\chapter{Seven}
\chapter{Eight}
\section{Eight-one}
\section{Eight-two}
\end{document}
It is also possible to use package tocbasic (which is part of the KOMA-Script bundle) with a standard class. Then you can use
\usepackage{tocbasic}[2017/01/03]% needs version 3.22
\DeclareTOCStyleEntry[dynnumwidth]{tocline}{chapter}
\DeclareTOCStyleEntry[dynnumwidth]{tocline}{section}

or
\usepackage{tocbasic}[2016/05/10]
\DeclareTOCStyleEntry[numwidth=2.6em]{tocline}{chapter}
\DeclareTOCStyleEntry[indent=2.6em,numwidth=3.2em]{tocline}{section}

Code:
\documentclass{report}
\renewcommand*\thechapter{\Roman{chapter}}
\usepackage{tocbasic}[2016/05/10]
\DeclareTOCStyleEntry[numwidth=2.6em]{tocline}{chapter}
\DeclareTOCStyleEntry[indent=2.6em,numwidth=3.2em]{tocline}{section}
\begin{document}
\tableofcontents
\setcounter{chapter}{6} % Problem starts at chapter 7
\chapter{Seven}
\chapter{Eight}
\section{Eight-one}
\section{Eight-two}
\end{document}
scrreprtmay be easier. A solution forreportdoesn't necessarily have to be the best for scrreprt. – Stefan Kottwitz Dec 19 '10 at 17:38screprt. I didn’t find a solution in the KOMA documentation, though. – Konrad Rudolph Dec 19 '10 at 18:02memoirsolution, seememoir: Roman chapters in ToC – Werner Dec 16 '20 at 04:44titletoc. – Dec 19 '10 at 16:52