Depends on what you mean precisely by "mixture of colors". You can use a path fading (cf. this answer) to e.g. achieve
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fadings,shadings}
\usepackage{fontawesome5}
\newcommand{\ShadeChar}[2][]{%
\begin{tikzfadingfrompicture}[name=temp]
\node[transparent!0] {#2};
\end{tikzfadingfrompicture}%
\tikz[baseline=(X.base)]{\node[inner sep=0pt,outer sep=0pt] (X)
{\phantom{#2}};
\path[path fading=temp,fit fading=false,overlay,#1] (X.south west) rectangle
(X.north east);}%
}
\begin{document}
\ShadeChar[upper left=red,lower right=blue]{\faVolleyballBall}
\begin{tikzfadingfrompicture}[name=temp]
\node[transparent!0] {\faVolleyballBall};
\end{tikzfadingfrompicture}%
\tikz[baseline=(X.base)]{\node[inner sep=0pt,outer sep=0pt] (X)
{\phantom{\faVolleyballBall}};
\path[path fading=temp,fit fading=false,overlay,fill=red]
(0:1em) arc(0:120:1em) to[bend left=20] (0,0) to[bend right=20] cycle;
\path[path fading=temp,fit fading=false,overlay,fill=blue]
(120:1em) arc(120:240:1em) to[bend left=20] (0,0) to[bend right=20] cycle;
\path[path fading=temp,fit fading=false,overlay,fill=green!70!black] (240:1em) arc(240:360:1em)
to[bend left=20] (0,0) to[bend right=20] cycle;}%
\end{document}

As you can see in the second example there is some tuning required because this trick only allows you to shade the whole character, and is ignorant about single patches of the character. Other packages like asymptote or pstricks allow you to retrieve the contour paths of glyphs, and to use them for e.g. filling.
Schrödinger's catin his/her answer. – Aug 19 '19 at 20:42