The Medrash on this weeks parsha (Bereishis) discusses this issue. The medrash has 2 opinions, 1 opinion seems to state that there is no divorce for non-Jews (or alternatively the medrash means that there is no formal divorce procedure) while the second opinion states that either side (husband or wife) can initiate a divorce. A similar discussion occurs in the Yerushalmi at the beginning of Kiddushin.
The Rambam (Hilchos Melachim 9:8)paskens that there is no formal divorce procedure and either side can initiate the divorce. This is difficult because he seems to pasken like both opinions.
The Ran in his chiddushim on Sanhefdrin (48b) quotes the Rambam and then quotes Rabbenu Dovid who disagrees and states that there is no divorce for non-Jews like the simple reading of the medrash and the Yerushalmi.
The Pnei Yehoshua also holds that there is no divorce for non-Jews but he goes further he states (Kiddushin 13b) that even the death of the husband does not free the women, the husbands death is a chiddush of teh Torah for Jews and therefore does not apply to non-Jews, this is how he wants to explain Yehuda and Tamar.
In summary, there is a dispute whether non-Jews can get dicorced, according to the Rambam (and this seems to be the accepted opinion) they can informally while according to a minority of Rishonim and Acharonim they are stuck, once a woman marries she is stuck for life.