Different versions of \theta

Here, I think there is a solution using \MTgreekfont{lmtt}\Mathastext: this code is taken here http://jf.burnol.free.fr/showcase.html (there are many solutions) and I have put also the italic option.

\documentclass{elsarticle}
\usepackage[LGRgreek,italic]{mathastext}
\MTgreekfont{lmtt}\Mathastext
\begin{document}
$0^{\circ}\leq \theta \leq 180^{\circ}$
\end{document}

The answer by Sebastiano uses the teletype font (lmtt) for the theta. There are some alternatives with other font styles.

Use the basic option for mathastext, which causes the package to only influence digits and Latin letters, resulting in the default math theta (but it limits the functionality of mathastext):

\documentclass{elsarticle}
\usepackage{gensymb}
\usepackage[basic]{mathastext}
\begin{document}
$0\degree \leq\theta\leq 180\degree$
\end{document}

Using the symbolgreek option, which uses the Symbol font for Greek:

\documentclass{elsarticle}
\usepackage{gensymb}
\usepackage[symbolgreek]{mathastext}
\begin{document}
$0\degree \leq\theta\leq 180\degree$
\end{document}

Redefining only \theta according to the default LaTeX definition, resulting in the default (math italic) theta (but it does not limit the functionality of mathastext):

\documentclass{elsarticle}
\usepackage{gensymb}
\usepackage[LGRgreek]{mathastext}
\mathchardef\theta="112
\begin{document}
$0\degree \leq\theta\leq 180\degree$
\end{document}