  We report the preparation of exactly one $^{87}$Rb atom and one $^{133}$Cs
atom in the same optical tweezer as the essential first step towards the
construction of a tweezer array of individually trapped $^{87}$Rb$^{133}$Cs
molecules. Through careful selection of the tweezer wavelengths, we show how to
engineer species-selective trapping potentials suitable for high-fidelity
preparation of Rb $+$ Cs atom pairs. Using a wavelength of 814~nm to trap Rb
and 938~nm to trap Cs, we achieve loading probabilities of $0.508(6)$ for Rb
and $0.547(6)$ for Cs using standard red-detuned molasses cooling. Loading the
traps sequentially yields exactly one Rb and one Cs atom in $28.4(6)\,\%$ of
experimental runs. Using a combination of an acousto-optic deflector and a
piezo-controlled mirror to control the relative position of the tweezers, we
merge the two tweezers, retaining the atom pair with a probability of
$0.99^{(+0.01)}_{(-0.02)}$. We use this capability to study
hyperfine-state-dependent collisions of Rb and Cs in the combined tweezer and
compare the measured two-body loss rates with coupled-channel quantum
scattering calculations.
