How to determine the phase of a time-sampled periodic signal?
You could try to Fourier transform,

$F(k) = \int_{-\infty}^{\infty} x(t) e^{-2\pi i kt} dt$

which can be expressed in terms of magnitude and phase in the following way

$F(k) = |F(k)|e^{i\Phi(k)} = a(k) + ib(k)$

with magnitude $|F(k)|$ and phase $\Phi(k) = \tan^{-1}(\frac{b}{a})$ for each frequency component $k$. Since it looks like you have a dominant $k$ representing your sine wave you can find the phase of that wave pretty easily. There are probably more obvious ways than this though.