[Edit: In case it is not obvious, x is the original signal, and y is the phase-shifted signal.]
Since you are working with I-Q signals, make an I and Q signal that are 90 degrees apart, since this is what In-phase and Quadrature mean. In the example below, a phase shift of -60 degrees is applied.
dt=1e-2; t=(0:99)*dt; % time vec tor (s)
T=0.2; % period (s)
x=cos(2*pi*t/T)+1i*sin(2*pi*t/T);
% Apply phase shift
phi=-pi/3;
y=x*exp(1i*phi);
% Plot results
figure
plot(t,real(x),'-r',t,imag(x),'-b',t,real(y),'--r',t,imag(y),'--b');
legend('x_{Real}','x_{Imag}','y_{Real}','y_{Imag}');
xlabel('Time (s)'); ylabel('Amplitude')
Looks reasonable. Good luck.
