Summary: When studying a kanji, native Japanese speakers often trace its strokes with their fingers on the air, palm, or thigh, while keeping their eyes fixed on the source model. (They do it for recalling, too, often closing the eyes or averting the gaze). This is called “air writing” (kūsho 空書 or karagaki 空書き). Thomas experimented with 75 non-native learners, of 22 different mother languages, and found that air writing helped retention significantly more (p < 0.01) than pen writing or visual memorization—though the effect size was modest, and only noticeable when memorizing harder kanji (some 15.43% more hits for the hardest kanji set).
Interestingly, six participants who were told to not use kūsho still did it spontaneously during recall tasks; either with their hands, or by mimicking kūsho patterns with subtle head or torso movements.
Thomas tested only kanji recall, not recognition (which is likely the most important task in the modern age). However, she does mention a couple studies suggesting that native speakers can recognize kanji more easily when allowed to air-write (Matsuo et al, Dissociation of writing processes: functional magnetic resonance imaging during writing of Japanese ideographic characters, 2000; and Matsuo et al, Finger movements lighten neural loads in the recognition of ideographic characters, 2003).
I think it’s reasonable to suppose that, for non-native learners, too, air-writing helps with both recall & recognition. This is good news because you can practice anywhere with your own body.