Using the \int_step_function

To use \int_step_function:nnnN here, you would first need some way to convert the integer to a dimension for the radius. Much easier here is to use \dim_step_function:nnnN, since you need a dimension.

To use \dim_step_function:nnnN you need to make \draw_path_circle:nn { 0 , 0 }{ <radius> } into a single (one-token, or N-type) macro that takes the <radius> as argument, so

\cs_new_protected:Npn \mathicon_circle_origin:n #1
  { \draw_path_circle:nn { 0 , 0 } {#1} }

then use as

% \dim_step_function:nnnN { begin } {  step  } {  end  } \function
  \dim_step_function:nnnN { 0.5ex } { 0.25ex } { 1.0ex } \mathicon_circle_origin:n

Though if it's a one off, you can also use the inline version:

% \dim_step_inline:nnnn { begin } {  step  } {  end  } { inline function }
  \dim_step_inline:nnnn { 0.5ex } { 0.25ex } { 1.0ex } { \draw_path_circle:nn { 0 , 0 } {#1} }

Here's the full code:

\documentclass[letterpaper]{article}
\usepackage{l3draw}

\ExplSyntaxOn
\NewDocumentCommand{\miconcentric}{ O{0.08ex} }
  {
    \mathicon_concentric_circles:n {#1}
  }
\cs_new_protected:Nn \mathicon_concentric_circles:n
  {
    \draw_begin:
    \draw_linewidth:n { #1 }
    % This
    \dim_step_inline:nnnn { 0.5ex } { 0.25ex } { 1.0ex }
      { \draw_path_circle:nn { 0 , 0 } {##1} }
    % or this and the definition below
    % \dim_step_function:nnnN { 0.5ex } { 0.25ex } { 1.0ex }
    %   \mathicon_circle_origin:n
    %
    \draw_path_use_clear:n { stroke }
    \draw_end:
  }
\cs_new_protected:Npn \mathicon_circle_origin:n #1
  { \draw_path_circle:nn { 0 , 0 } {#1} }
\ExplSyntaxOff

\begin{document}
    Sample \miconcentric
\end{document}

In this special case where the dimensions are integral multiples of a base one, namely 0.25ex, with \int_step_inline:nnn it's easy:

\documentclass[letterpaper]{article}
\usepackage{l3draw}

\ExplSyntaxOn

\NewDocumentCommand{\miconcentric}{ O{0.08ex} }
 {
  \mathicon_concentric_circles:n { #1 }
 }
     
\cs_new_protected:Nn \mathicon_concentric_circles:n
 {
 \draw_begin:
 \draw_linewidth:n { #1 }
 \int_step_inline:nnn { 2 } { 4 }
  {
   \draw_path_circle:nn { 0 , 0 } { 0.25ex * ##1 }
  }
 \draw_path_use_clear:n { stroke }
 \draw_end:
 }
\ExplSyntaxOff

\begin{document}

Sample \miconcentric

\medskip

\LARGE
Sample \miconcentric[0.1pt]

\end{document}