Phase shift of voltage across capacitor in series RC
In the book it says that the answer is -25 degrees


It means that the output sinewave voltage lags the input sinewave voltage by 25 degrees.

Phase lag = \$Tan^{-1}(\dfrac{R}{X_C})\$


  Using the tangent relationship between the capacitive reactance and
  resistance, I keep getting 65 degrees for an answer.


It sounds like you might be taking the arctan of Xc/R (67.08 degrees).