Circuitikz place text above and below component

Around the resistor are anchor points. You can name the resistor node using the n= style, the anchor point opposite the label is (normally) "s".

\documentclass[a4paper,journal]{IEEEtran}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[american]{circuitikz}


\begin{document}
\begin{circuitikz}[scale=1,transform shape]
\draw
% Left half of circuit.
(0,0)   to [sV, l=$v_\mathrm{s}$]           (0,2)
        to [short, -o]                      (1.5,2)
        to [R, l=$R_\mathrm{G}$, n=res, -o] (4,2)
        to [open, v^=$v_\mathrm{gs}$]       (4,0)
        to [short, o-o]                     (1.5,0)
        to [short]                          (0,0)

(1.5,0) node[below] {S}
(1.5,2) node[above] {G}
(res.s) node[below]{1k$\Omega$} %here is the added code
;
\end{circuitikz}
\end{document}