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.
It is not permissible to borrow money from a non-Islamic bank in order to get married because marriage is not the only way to avoid committing Zina (fornication or adultery). There are other matters that could be done to avoid Zina, among which is fasting. 'Abdullaah Ibn Mas'ood narrated that the Prophet said: "O young people! Whoever among you can marry, should marry, because it helps him lower his gaze and guard his modesty (i.e. his private parts from committing illegal sexual intercourse etc.), and whoever is not able to marry, should fast, as fasting diminishes his sexual desire." [Al-Bukhari and Muslim]
On the other hand, it is permissible for a person who fears to commit fornication or adultery to take a medicine that reduces his desires or eradicates it temporarily but it is not permissible to totally kill sexual desires forever, as this is considered like castration.
Sa'd Ibn Abu Waqqaas narrated that "The Prophet refused the idea of 'Uthmaan Ibn Math'oon about staying celibate; had the Prophet allowed him, we would have sought castration."[Al-Bukhari and Muslim]
Moreover, you have to stay away from places of temptation and affliction and lower your gaze from looking at what arouses your desires. Allaah says (what means): {And tell the believing men to lower their gaze (from looking at forbidden things) and protect their private parts (from illegal sexual acts, etc.). That is purer for them. Verily Allaah is All-Aware of what they do.}[Quran 24:30]
Besides, you should be patient and keep company with righteous men and supplicate to Allaah to facilitate marriage for you. Allaah says (what means): {And let those who find not the financial means for marriage keep themselves chaste, until Allaah enriches them of His Bounty...}[Quran 24:33]
Allaah further says (what means): {And for those who fear Allaah, He (ever) prepares a way out and he provides for him from (sources) he never could expect.} [Quran 65:2-3]
Finally, you should know that the sin of dealing with Riba is much worse and much greater than committing fornication or adultery. 'Abdullaah Ibn Hanthalah narrated that the Prophet said: "Knowingly consuming a Dirham of usury/interest is worse for a man than committing adultery thirty-six times."[Ahmad and Ad-Daaraqutni]
Therefore, we advise you to be patient until Allaah makes a way out for you, but do not get a loan with Riba as this is declaring a war against Allaah.
Allaah Knows best.