Well, I don't know of any method to snap them directly but you can try with shear and custom orientations.
Here is how :

I have here a cylinder and a slanted plane. Select the Plane, go to edit mode and select the face you want to snap the vertices on (in my case I only have one face :D ), then on the header of the viewport, select Normal
for Transform orientation
:


As you can see, you have the z axis pointing along the normal of the plane. Create a custom Transform orientation
from this with the little +
near the Transform orientations list (Make sure you have Normal
as selected Transform orientation
before this):

You have now a custom transform orientation named Face
that follows the direction of the plane, you can rename it if you want. For now, select Global
to go back to the default transform orientation.
Now go back to Object Mode and select the cylinder, go to edit mode and select the vertex you want to snap, go to Front View orthographic and set the shading mode to Wireframe :

Now, you will "shear" the vertices to roughly get the orientation of the plane, it doesn't need to be perfect, just as close as you can :

You can do this with CTRL + SHIFT + ALT + S or by going to Mesh > Transform > Shear
:

As a side note, when you shear some geometry, you can chose what direction you shear it by pressing X or Y after pressing the shortcut. For my case, it's the default X.
With that done, we can select the custom orientation we created in the Transform Orientations option :

And just scale the selected vertices on the z axis to 0 by going S then Z then 0 then Enter. This will align the vertices perfectly to the plane. All that is left to do is move them to the plane and we can now snap them with the snap to face option in the header :

The easiest way (and the most accurate way) to do that is to select Global orientation, move them on the X axis with snap to face on and they should snap perfectly to the face while staying in line with the cylinder's direction.