What is the theme of "The Moving Finger"?

The theme of "The Moving Finger" is generally regarded as relating to control. Ralph's first wife controls him so thoroughly that he is compared to the host for a parasite. He loses himself entirely; he isn't even aware of himself until she passes.
When Ralph marries the second Mrs. Grancy, he lives his fullest life through his happiness with her. If he is to be believed, the relationship was truly mutual, and they were both so overcome with joy at their union that their unexpected and sudden separation when she died was almost incomprehensible to Ralph Grancy. He realizes, through her continued "presence" in his life (it is not clear in the story if this presence was real or imagined), that he needs to bring her along, so to speak, into old age so that she will not be alone without him, even in death. This is why Ralph asks Claydon to age the masterpiece he painted of Mrs. Grancy—so that the couple can, in a way, grow old together.
Claydon believes himself to be in love with Mrs. Grancy, though the reader is given no clear indication that those feelings were ever returned. What both men share is a love for this woman that becomes obsession. Whether there is a paranormal occurrence that allows Mrs. Grancy to take hold of these men in the afterlife, or their fantasies grip them to the point of delusion, Mrs. Grancy has a firm hold on both men. Claydon uses his innate knowledge of Mrs. Grancy, and Ralph's desire to continue experiencing his life with her, to nudge him into death with merely a look upon the portrait's face. This is how Claydon comes to own Mrs. Grancy (the portrait) once and for all, remaking her back into his ideal image of her.
This control is nuanced; neither man is trying to control or manipulate Mrs. Grancy as she was when living. They have literally objectified her, projecting all their fantasies onto a portrait. Ralph Grancy idealizes unyielding companionship. Claydon idealizes the point in a woman's beauty when youth has ripened into womanhood, where innocence and experience exist in balance.
Both men want so badly to seize onto how Mrs. Grancy made them feel in those moments that they wanted her frozen at those moments in time—not because they desire to own the woman, but because they feel compelled to own those fleeting moments when they saw themselves idealized in her. They were chasing their own reflections in her face, like wanting to catch time in a jar.

One important clue to the story's theme is the title, "The Moving Finger." This is a quotation from a poem that was very familiar in Edith Wharton's day. Her story was published in 1885.
The phrase is part of one of the most well known passages of Edward Fitzgerald's 1859 translation (really, a liberal interpretation) into English of parts of The Rubáiyát of Omar Khayyam. Khayyam was an eleventh and twelfth century Persian astronomer, mathematician, and poet. His long poem was popular in artistic and intellectual circles in both England and the U.S.

The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it.

The idea is that fate or time moves with its own force and that no human action--whether based in faith or intellect or emotion--will have any effect on that.
The theme of these lines and the story is that we cannot change the past or the future.
Both Ralph Grancy and Claydon tried to alter reality, the former by asking that Mrs. Grancy's portrait be aged and the latter by doing the work. While the narrator is horrified at Claydon's actions, the artist is correct that his actions did not kill Glancy. The moving finger simply wrote its unchangeable story.
http://classics.mit.edu/Khayyam/rubaiyat.html

One of the themes of "The Moving Finger" by Edith Wharton is control—or, rather, the lack of it. However hard he tries, Ralph just can't seem to move on with his life. His sense of loss at the death of his second wife is ever present and haunts his every waking hour. Ralph is controlled by his past. As he cannot break free from the memory of the second Mrs. Grancy, Ralph tries desperately to exert some control of his own. There is a hint that perhaps Ralph's second wife had an affair with Claydon, the portrait painter. For Ralph, this must have represented a considerable loss of control over his life. One could argue, then, that in getting Claydon to repaint Mrs. Grancy's portrait to make her look older, Ralph is taking back some of the control he lost when his wife cheated on him.