Why is an RC circuit a first order system?
The order of system gives the number of memory storing elements in the circuit.

What you have written above is a KVL equation of the circuit. But when you determine the order of the system you need to find the transfer function of the system. Laplace domain is normally used. The highest power of $s$ in  the denominator in a strictly proper transfer function gives the order of the system.

So in the $s$-domain,say you take the output across the capacitor,

$\dfrac{V_o(s)}{V_i(s)} = \dfrac{\frac{1}{sC}}{R+\frac{1}{sC}}$

simplifying we get 

$\dfrac{V_o(s)}{V_i(s)}= H(s)=\dfrac{\frac{1}{RC}}{s+\frac{1}{RC}}$

So the highest power of $s$ is given by 1. So the order of the system is 1.