\documentclass{article}
\makeatletter
\usepackage{tikz}
\usetikzlibrary{calc}
% #1 is a multiplier of fontsize for the minimum diameter of the circle
% #2 is the symbol to be circled.
\newcommand*\circled[2][1.6]{\tikz[baseline=(char.base)]{
\node[shape=circle, draw, inner sep=1pt,
minimum height={#1\dimexpr\f@size\relax\f@size*#1},] (char) {\vphantom{WAH1g}#2};}}
\makeatother
\begin{document}
This is a \circled{*} and a \circled{$\star$} and a \circled{$\ast$}.
This is a \circled[1.2]{*} and a \circled[1.2]{$\star$} and a \circled[1.2]{$\ast$}
This is a \circled[0.8]{*} and a \circled[0.8]{$\star$} and a \circled[0.8]{$\ast$}
\end{document}

You can have other options too like:
\documentclass{article}
\makeatletter
\usepackage{tikz}
% #1 is a multiplier of fontsize for the minimum diameter of the circle
% #2 is the symbol to be circled.
\newcommand*\circled[2][1.6]{\tikz[baseline=(char.base)]{
\node[shape=circle, draw, inner sep=1pt,
minimum height={\dimexpr#1\f@size\relax},] (char) {\vphantom{WAH1g}#2};}}
\newcommand*\bcircled[2][6pt]{\tikz[baseline=(char.base)]{
\node[shape=circle, draw, inner sep=1pt,
minimum height={#1},] (char) {#2};}}
\makeatother
\newcommand*\ccircled[2][6pt]{\tikz[]{
\node[shape=circle, draw, inner sep=1pt,
minimum height={#1},] (char) {#2};}}
\makeatother
\begin{document}
A) This is a \circled{*} and a \circled{$\star$} and a \circled{$\ast$}.
This is a \circled[1.2]{*} and a \circled[1.2]{$\star$} and a \circled[1.2]{$\ast$}
This is a \circled[0.8]{*} and a \circled[0.8]{$\star$} and a \circled[0.8]{$\ast$}
B) This is a \bcircled{*} and a \bcircled{$\star$} and a \bcircled{$\ast$}.
This is a \bcircled[12pt]{*} and a \bcircled[12pt]{$\star$} and a \bcircled[12pt]{$\ast$}
This is a \bcircled[16pt]{*} and a \bcircled[16pt]{$\star$} and a \bcircled[16pt]{$\ast$}
C) This is a \ccircled{*} and a \ccircled{$\star$} and a \bcircled{$\ast$}.
This is a \ccircled[12pt]{*} and a \ccircled[12pt]{$\star$} and a \bcircled[12pt]{$\ast$}
This is a \ccircled[16pt]{*} and a \ccircled[16pt]{$\star$} and a \ccircled[16pt]{$\ast$}
\end{document}
That gives:
