{{0°, 222597.}, {10°, 215256.}, {20°, 205889.}, {30°, 190917.},
{40°, 173117.}, {50°, 154249.}, {60°, 138540.}, {70°, 125409.},
{80°, 116973.}, {90°, 112937.}}

data = {{0°, 222597.}, {10°, 215256.}, {20°, 205889.}, {30°, 190917.},
       {40°, 173117.}, {50°, 154249.}, {60°, 138540.}, {70°, 125409.},
       {80°, 116973.}, {90°, 112937.}}
intensityList = data[[All, 2]

model = a Cos[b + 10°*x]^2 + c;
fittingParameter = FindFit[intensityList, {model}, {a, b, c}, x]

p2 = Plot[{a Cos[b+x]^2 + c} /. fittingParameter, {x, -0.1, 3.2}];
p1 = ListPlot[data];
Show[p1, p2]