\documentclass{article}
\usepackage[english]{babel}
\usepackage[]{circuitikz}
\usepackage{amssymb}
\begin{document}
\begin{circuitikz}
\draw(0,0)
node [scale=6,thick]{$\circlearrowright$}
(0,0) node{$I_1$};
\end{circuitikz}
\end{document}


Yields:

I would like the arrowhead to be filled in like this:

I'm sure there's already something about this here. Certainly several examples on using arrows with TikZ can be found... But arrows are specified as an option to the \draw command. If you say \draw[->] whatever you tell LaTeX to draw there's going to be an arrow head at the end.

Furthermore there are a lot of arrow tips available to be used, the Default one from tikz is something like the one you have shown so you have to specify one that suits your Needs. Check the manual under Part III, Arrows. There's also the arrows.meta library that lets you customize arrow tips.

Here's an example that Shows how to draw what you want and three kinds of arrows, from left to right: tikz default arrow, LaTeX arrow and Stealth arrow.

\documentclass[border=2mm]{standalone}
\usepackage{circuitikz}
\begin{document}
\begin{circuitikz}
\draw[->] (0,0) node{$I_1$} ++(80:0.5) arc[start angle=80, delta angle=-350, radius=0.5];
\draw[-latex] (1.1,0) node{$I_1$} ++(80:0.5) arc[start angle=80, delta angle=-350, radius=0.5];
\draw[-stealth] (2.2,0) node{$I_1$} ++(80:0.5) arc[start angle=80, delta angle=-350, radius=0.5];
\end{circuitikz}
\end{document}