Dotted footnote rule

You're looking for \leaders. \leaders is a TeX primitive used to repeat a box until it fills some space. I used \xleaders here: the x stands for "expanded leaders", to ensure the dots are placed aligned with the margins.

I added three customisation points: \fnoterulesep is the distance between two consecutive dots, and \fnoterulechar is the character to be repeated. Here's an example with 2pt and .:

and here with 5pt and $\bullet$:

I also added a \fnoteruleaftersep to tweak the distance between the rule and the footnotes.

\documentclass[titlepage,paper=a4,11pt,onecolumn]{scrartcl} 
\usepackage[top=3cm, bottom=3.5cm, left=2.5cm, right=2.5cm]{geometry}
\usepackage[english]{babel}
\usepackage{blindtext}

\newlength\fnoterulesep
\setlength\fnoterulesep{2pt}
\newlength\fnoteruleaftersep
\setlength\fnoteruleaftersep{4pt}
\newcommand\fnoterulechar{.}
\renewcommand{\footnoterule}{%
  {\sbox0{\fnoterulechar\kern\fnoterulesep}%
   \par\vspace*{\dimexpr-\baselineskip+\ht0+\dp0-\fnoteruleaftersep}%
  \noindent
  \xleaders\hbox{%
    \fnoterulechar
    \kern\fnoterulesep}%
      \hfill\fnoterulechar
  \par \nointerlineskip
  \vspace*{\dimexpr-\ht0-\dp0+\fnoteruleaftersep}}%
}

\begin{document}

\section{Introduction}
This a piece of text with a footnote here\footnote{This is my footnote} for testing purposes.

\blindtext[2]

\end{document}

Is this what you want?

\documentclass[titlepage,paper=a4,11pt,onecolumn]{scrartcl}
\usepackage[top=3cm, bottom=3.5cm, hmargin=2.5cm]{geometry}
\usepackage[english]{babel}
\usepackage{blindtext}

\makeatletter
\renewcommand{\footnoterule}{%
  \kern -4.5pt
 \vbox to 0.5pt{\hbox to \textwidth{\leaders\hbox{\kern 4pt .\kern 4pt}\hfil}\vss}
  \kern 4pt
}
\makeatother
\begin{document}

\vspace*{12cm}

\section{Introduction}
This a piece of text with a footnote here\footnote{This is my footnote} for testing purposes.
\blindtext[2]

\end{document}