There is no stated du`a that is uttered to help one get married to a certain person. However, one can generally ask Allah using any formula of du`a to help him get married to a certain person such as, ‘ O Allah! help me get married to such and such person etc..’
Moreover, one should take practical steps along the way of supplication such as seeking the help of experienced and religiously committed people and inquiring about the person’s morals.
Having said this, one is also recommended to reiterate general supplications which help one fulfill one’s needs such as:
Yaa hayyu yaa qayyoomu bi rahmatika astagheethu.
(O the Ever-Living, the Self-Subsisting Source of all beings, I beseech Your Mercy, so have mercy on me.)
Rabbi innee bimaa anzalta ilayya min khayrin faqeer.
(O Lord, I remain ever in need of any good that You may send my way.)