All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Muslim scholars held different opinions regarding making a vow to do a permissible act. Imaam Ahmad believed that the person, in this case, has the choice either to deliver on his vow or to offer expiation like for breaking an oath, analogical to the case of an oath. Other scholars believe that when a person makes a vow to do a permissible act, it is not considered a valid, binding vow and it is not incumbent on him to do anything. Some of the early jurists who adopted that opinion mentioned marriage as an example of this kind of vow. Ad-Dusooqi said,
"A vow is considered binding only when the person makes a vow to do an act that is recommended in all cases and times. This means that when one makes a vow to do an act that is sometimes permissible, sometimes recommended, and sometimes forbidden, such as marriage and giving gifts, such a vow is not considered binding." [Hashiyat Ad-Dusooqi]
Shaafi‘i jurists held different opinions as to whether the person is required to fulfill a vow to get married or not. Some believed that the person is obliged to get married in this case as he had vowed, while others considered such a vow not binding. You can refer to Asna Al-Matalib.
Thus, the questioner comes to know that it is not incumbent on him to get married as per his vow. If he offers expiation like for breaking an oath, it will be better according to Imaam Ahmad's opinion.
Allaah Knows best.