There is angular momentum in the orbit of one body around another, as well as in the rotation of the body around its own axis.
The earth has angular momentum with respect to the sun both through its 24-hour rotational period and its 365-day orbital period.
The AM of the orbital motion is far greater than that of thre daily rotation.
Angular momentum of the earth due to the 24-hour period is around 7.1 x 10^33 kg m^2 s^-1
Angular momentum of the earth due to the orbit around the sun is around 2.7 x 10^40 kg m^2 s^-1 (around 5 million times greater)
https://www.vanderbilt.edu/AnS/physics/astrocourses/ast201/angular_momentum.html
If the falling body transitions from largely linear motion to elliptical/hyperbolic motion (orbiting), the body gains angular momentum.
Where does that comes from?
The large massive body transfers some of its AM to the smaller body.
That can be seen through the orbital slingshot of a spacecraft, in which the spacecraft accelerates, at the expense of (a very small part of) the rotational momentum of the planet around which it slingshots.
Hope it helps