Answer
About 0.4 grams per year.
Work Step by Step
If 960 watts is the average power for a year, find the amount of energy.
$$\frac{960J}{s}\frac{3.156\times10^7s}{year}\frac{MeV}{1.60\times10^{-13}J}=1.894\times10^{23}MeV/y$$
Change this to an amount of uranium.
$$\frac{ 1.894\times10^{23}MeV}{y}\frac{1fission}{200\;MeV}\frac{235g}{6.02\times10^{23}atoms}\approx 0.4g/y$$
