the resulting pdf of a vector of $N$ observations, $\pmb{x}$ will be the product of the individual pdfs, i.e.

$f_{\theta}(\pmb{x},p)=\displaystyle{\prod_{n=1}^N} \dfrac{x_n^{p-1}e^{-\frac{x_n}{\theta}}}{\theta^{Np} ~~ \left( \Gamma(p) \right)^n}$

to find the maximum likelihood estimate of $\theta$ take the derivative with respect to $\theta$ of $\ln\left(f_{\theta}(\pmb{x},p) \right)$

set it equal to $0$ and solve for $\theta$

The resulting MLE is a pretty simple form.