Modify arraystretch for a single row in table

The best solution is to use the cellspace package: it defines an adjustable minimal vertical padding around a cell. For this, you have to prefix the column specifier with the letter S (or C if you load siunitx).

With \arraystretch, there are two drawbacks: first the cell contents is no more vertically centred, and second, you have to determine, by trial and error, the stretch value – any modification of the contents may result in a new value, as is demonstrated in the following, where I modified one fraction, keeping the value you gave:

\documentclass{article}

\usepackage{amsmath}
\usepackage{booktabs, cellspace, hhline}
\setlength\cellspacetoplimit{4pt}
\setlength\cellspacebottomlimit{4pt}

\begin{document}

\begin{table}
  \renewcommand{\arraystretch}{2.3}
  \begin{tabular}{@{}c|l@{}}
    \bfseries $R_x$ & Symbol \\
    \hline\hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B} $ \\
    \hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B + \cfrac{C}{D}} $ \\
    \hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B} $ \\
    \hline
  \end{tabular}
\hskip2cm
  \begin{tabular}{@{}Sc|Sl@{}}
    \bfseries $R_x$ & Symbol \\
    \hline\hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B} $ \\
    \hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B + \cfrac{C}{D}} $ \\
    \hline
    $\dfrac{a}{b}$ & $ \dfrac{A}{B} $ \\
    \hline
  \end{tabular}
\end{table}
\end{document} 

Similar result as with cellspace package, as propose Bernard, you can obtain with makecell package:

\documentclass{article}
\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{wrapfig}

\usepackage{makecell}% <-- for gaped cells

\begin{document}

\begin{wrapfigure}[14]{R}{8.5cm}
\setcellgapes{3pt}
\makegapedcells
    \begin{tabular}{@{}>{$\displaystyle}c<{$}|>{$\displaystyle}l<{$}@{}}
R_x                 &   \text{Symbol}           \\
    \hline\hline
\frac{a}{b}         &   \frac{A}{B}             \\
    \hline
\text{some text}    &   \text{some other text}  \\
    \hline
\frac{a}{b}         &   \frac{A}{B}             \\
    \hline
\frac{a}{b}         &   \frac{A}{B}             \\
    \hline
    \end{tabular}
\end{wrapfigure}
\end{document}

Note: Also \makegapedcells doesn't work in all circumstances. For example, it prevent coloring rows/columns with use \colortbl or [table]{xcolor} packages.