The 27-year-old was named in the Scorpions' squad for their game against South Sudan on 14 June.
Khan had never played at a level above the National League before joining the Robins last summer.
He made 35 appearances for the League Two club this season.
"It means everything," Khan told BBC Radio Wiltshire.
"Growing up in Gambia the national team, I think back then, was everyone's way out. All you think is I want to do well so I can play for the junior national team and do well for them and get scouted and go to Europe.
"It was everyone's main dream to play for the national team."
A scout from the Gambian team came to watch Khan play, although he did not believe it would lead to a call-up to the squad.
"The coach then called me [but] even then I thought there's a lot of Gambian players abroad so it might not happen.
"Later on, just a couple of days after the end of the season, I went to go and do some fitness with my friends and after the session I've gone on WhatsApp and seen I was in the Gambia national team group chat. I thought 'wow'."
Khan began his career in the lower leagues of the English football pyramid, eventually joining Dagenham & Redbridge and then Chesterfield in the National League in 2021.
He eventually made the step up to the English Football League when he joined Swindon, aged 26, and said he had a "point to prove" to himself that he could play at that level - having progressed later than his contemporaries.
"It was a massive step for me and I enjoyed every bit of it," Khan said of last season.
Gambia sit third in Group G of their AFCON qualification group with two games remaining.
"I thought the best opportunity I can give myself to play for them is to do as well as I can in England, and if I do I'll play for them it's a dream, it's amazing, I can't believe it," he added.
Source: BB
