Solution 1 (Best)
This is a solution I made using frabjous suggestion using tocloft and titlesec.
There is a hack using the let command and titlesec package for managing titles.
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{tocloft}
\usepackage[explicit]{titlesec}
\let\theRpart\thepart
\renewcommand{\thepart}{\hbox to 4em{\Roman{part}}}
\newcommand{\partfont}{ \fontsize{30pt}{36pt} \bfseries \selectfont }
\titleformat{\part}[display]
{ \partfont }
{ \ \vspace{35pt} \\ \filleft \partname \ \theRpart}
{15pt}
{ \filleft #1}
[\vspace{100pt}]
\begin{document}
\tableofcontents
\part{Part1}
This is a part
\newpage
\part{Part2}
This is a part
\newpage
\part{Part3}
This is a part
\newpage
\part{Part4}
This is a part
\newpage
\part{Part5}
This is a part
\newpage
\part{Part6}
This is a part
\newpage
\end{document}
Solution 2 (failed)
The solution above is a kind of hack. It would be great if one could achieve it with titletoc package, however I do think that titletoc just like tocloft has problems with part in article class.
Just a general not refined example:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{tocloft}
\usepackage[explicit]{titlesec}
\usepackage{titletoc}
\let\theRpart\thepart
%\renewcommand{\thepart}{\hbox to 4em{\Roman{part}}}
\newcommand{\partfont}{ \fontsize{30pt}{36pt} \bfseries \selectfont }
\titleformat{\part}[display]
{ \partfont }
{ \ \vspace{35pt} \\ \filleft \partname \ \theRpart}
{15pt}
{ \filleft #1}
[\vspace{100pt}]
\titlecontents{section}[1.5em]{\vspace{40pt}}{ \contentslabel{2.3em} }{ }{after }[]
\titlecontents{part}[1.5em]{\vspace{40pt}}{ \contentslabel{2.3em} }{ }{after }[]
\begin{document}
\tableofcontents
\part{Part1}
This is a part
\section{ASDF}
\newpage
\part{Part2}
This is a part
\newpage
\part{Part3}
This is a part
\newpage
\part{Part4}
This is a part
\newpage
\part{Part5}
This is a part
\newpage
\part{Part6}
This is a part
\newpage
\end{document}
So in my opinion the hack that was created with frabjous suggestion is the only known valid way.
Solution 3 (failed)
I was also trying :
\let\oldthepart\thepart
\renewcommand{\thepart}{...} %modified
\tableofcontents
\renewcommand{\thepart}{\oldthepart} %back to normal
But it failed miserably ;]
Solution 4 (success)
One could however in the first run of latex run with command changing the hbox and the last run (when attaching TOC) without renewing \thepart command if one doesn't have the time to read into titlesec package.
Summary
However the let command with titlesec package is the best solution in my opinion.
I'm leaving this question open for the time being.