Why do I get these voltage offsets when modeling an RC circuit with an AC voltage source?
there are things that the circuit can do and some things it cannot do, let's start at t=0 the source voltage(your cosine function) is providing positive voltage after the voltage drops below 2 the capacitor cannot charge above that, and now it is discharging, now with more time it reached a higher voltage.

you have the derivative of the charge there, also known as the current that shows this. See how the current is almost 0 at the first peak of the capacitor voltage? that means it is not charging up anymore. Now your current is ideal, but not completely correct, it is ignoring the resistor as you have it written so this will also have it slightly off.

With a capacitor this huge though the resistor effect is very small but still there, so I think if you properly take that into account the current waveform will match better with reality(it is almost perfect)

I suggest you use microFarads so you get a more realistic response of charge discharge transients, 1F is ridicously large. The math all works the same, but I think it makes lots of things hard to match with reality.