Add an offset of 2.5 V to analog signal
The problem is that you have connected your voltage sources in parallel. The source impedance of your voltage divider is 50 kΩ, while the impedance of your AC source is zero. When you connect these in parallel, the AC source shorts out the DC source, and you get zero offset.
If you want to add voltages, you need to connect them in series. Connect V1 between the junction of the two resistors and the scope.
However, in many applications, both sources need to be referenced to the same node (usually called &quot;ground&quot;). In that case, you can build a circuit that takes the &quot;average&quot; of the two voltages, which includes the operation of adding them together. To do this, they need to have the same source impedance. Take your original circuit and add a 50 kΩ resistor in series with V1. But in this case, both voltages also get divided by two, giving you a 0.5 V AC signal with a 1.25 V DC bias.
Or you can use an impedance that varies with frequency as G36 suggested in a comment, such as a capacitor. This creates a high-pass filter for the AC signal, and a low-pass filter for the DC bias. With the correct selection of component values, neither signal is significantly attenuated.