A natural rock wall usually contains lines and crevices between the rocks. This is part of what gives it its natural look, but it can also be a problem, collecting dirt, debris and moisture in the cracks. By mortaring those joints, you can keep out the dirt while still generally keeping the natural look of the wall. A cement trowel will work, but requires a level of expertise that you may not have. Try a grout bag, which is designed to apply grout or mortar directly into spaces using the same process as a pastry bag.
Use your hand broom to brush out the spaces between the rocks in the wall.
Fill the grout bag with mortar, scooping it into the bag with a wooden spoon. Fill the bag just enough so there's still room to twist the top of the bag closed.
Set the tip of the bag into the space between the stones. Squeeze the bag with both hands while slowly dragging it backward, laying mortar into the space. The mortar should fill the space but not get onto the face of the rock.
Repeat the process for each space.
Dampen a sponge. Rub it gently over the mortar, smoothing and flattening it. Let it set for a day.
Gently brush your hand broom over the dry mortar to get rid of any residual dust and sand.