Amartey completed a move to the Turkish giants on a free transfer last month after parting ways with Leicester City.
And the centre-back has already hit the ground running, having started and scored in their Europa Conference League game against KF Tirana last week.
During his time at Leicester City, Amartey only scored three goals despite spending seven years at the English club.
However, the 28-year-old now aims to add more goals to his game after revelling his debut strike for Besiktas.
“I played seven years in Leicester, played 145 matches, I could only score three goals,” Amartey said, as quoted by Ghanaweb.
“I had a goal celebration in my first match here. Beşiktaş has been lucky for me. I will continue to search for goals in set pieces. I hope I continue to score goals like this."
Meanwhile, the Ghana international recently opened up on why he gifted a brand-new car to his childhood coach in Ghana.
According to him, the coach helped him a lot when he was 12, adding that such good people are rare in today’s world.
Earlier this year, the newly-signed Besiktas centre-back went viral after buying a car for a man who coached him while he was young.
Although Amartey himself was not in the country at the time, his team presented a Toyota Vitz to the said coach.
Having joined Turkish side Besiktas following the expiration of his contract at Leicester City, the Ghanaian explained his kind gesture.
"Yes, this news is true. He was my football coach in Ghana when I was 12. That is why I bought him the car. He was a good person because it is very difficult for someone to help you in Africa. He helped me a lot when I was young, he did everything he could. That's why I gave him a car,” Amartey said.