Squiggly arrows in tikz

It is possible, indeed. You can use the decorations.pathmorphing library for this, which allows very fine control over how your paths look:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{amssymb}

\begin{document}
$\rightsquigarrow$

\tikz \draw [->,
line join=round,
decorate, decoration={
    zigzag,
    segment length=4,
    amplitude=.9,post=lineto,
    post length=2pt
}]  (0,0) -- (0.3,0);
\end{document}