No - there is no way to do this on an RPi without additional hardware.
Neither the question, not the referenced documentation provide the magnitude of this sine wave. Without that information the additional hardware required can not be determined.
The OP has found some specifications on the amplitude of the sine wave output from the ac generator in the anemometer. Following are some thoughts on that:
1. Buy the Manufacturer's Interface Hardware
As it turns out, the anemometer manufacturer also manufactures and sells interfaces to the anemometer. The "Interface 40C to Logic Level, Speed Amp #892E" appears to be the easiest to use with a Raspberry Pi. According to the specifications, this interface could be powered from the RPi 3.3V supply, and connected directly to an appropriate GPIO pin configured as an input. You'll need to write software to count the transitions on the GPIO pin, and convert that to wind speed IAW the manufacturer's specifications; e.g. 100 Hz = 60 mph wind speed - or whatever that conversion is.
Knowing the manufacturer's specifications on the amplitude and other characteristics of the anemometer's ac generator enable a "Do-It-Yourself" approach to the interface. Complicating the design of an interface to the Raspberry Pi is the fact that RPi has no analog input. That is exacerbated by the variable amplitude characteristics of the ac generator used in this anemometer, and the fact that at the low end of its measurement range, the generator's output is 80 mV p-p.
That said, the design is not necessarily overly complex either, and probably well within the realm of we hobbyists. There are several/many ways to do this - one method is a "zero crossing detector" which is just a comparator with its REF input tied to GND. The schematic below turned up in a search - see this Application Note for further details.
The Raspberry Pi can source the 5V supply needed to bias the comparator.
Verify the output voltage before connecting it to your RPi GPIO as anything over 5V will likely destroy it.
Adjust the values of R1 and R2 to keep the maximum output voltage from the anemometer's AC generator to approximately 2.5V
Your software will need to monitor the GPIO pin you choose, count the transitions, and calculate the windspeed.
Finally, let us know if you decide to take this route, and have questions re the circuit.