Did I correctly use the Voltage divider rule to derive the transfer function?
Assuming that Rs is a short, the resistor is in parallel to an ideal voltage and can be omitted.

The resulting circuit is a simple RC highpass but the equation is for a lowpass.
As noted in the captain's comment the correct expression should be:  1 / (1/(jw *R3*C1) + 1)
which can be rewritten as
$$
A(j\omega)=\frac{j\omega R_3 C_1}{1 + jw R_3 C_1}
$$

The current through C1 and R3 is the same, where else should the current go?