Both "a tear rolled down my face" and "a tear ran down my face" are correct, but they convey slightly different nuances of emotion.
"A tear rolled down my face": This expression suggests a slow, gentle, and perhaps more controlled shedding of tears. It often implies a poignant or sentimental moment, where the tear falls gracefully and is usually associated with sadness, joy, or deep emotion.
"A tear ran down my face": This phrase implies a faster and less controlled flow of tears. It may suggest a stronger emotional reaction, such as overwhelming sadness, grief, or even tears of laughter. The use of "ran" gives a sense of the tear moving quickly.
In most cases, the choice between these two phrases depends on the writer's intent and the specific emotion or atmosphere they wish to convey. Both are valid options, so consider the context and emotional tone of the scene or situation you are describing to decide which expression fits best.