Perhaps this?

A[theta_] := 0.000219952 Csc[theta]^2 Sin[5.16831 Sin[theta]];

Plot[A[theta]^2, {theta, -90 Degree, 90 Degree}]

Does that appear to be doing what you were trying to accomplish?

If not then try explaining where you think I went wrong and we will try it again.

You may want to insert a, PlotRange->{stuff} just inside that last ] where "stuff" tells Mathematica what y range you want or what x and what y range you want. Look up PlotRange in the help system if the plot without the PlotRange doesn't include the parts you want to see. I also included the Degree because I am guessing from your 90 that you are using degrees for theta.