Marwa has served as a FIFA referee since 2011. He is the first Kenyan football official to be involved in any FIFA competition, having featured in the 2011 FIFA U-17 World Cup. He was named as an assistant referee in the 2012 and 2013 Africa Cup of Nations. Marwa was named as a reserve official at the 2014 FIFA World Cup and an assistant referee at the 2016 FIFA Club World Cup. He was included as CAF's assistant referee in the 2017 FIFA Confederations Cup, where he served alongside Bakary Gassama, Jean-Claude Birumushahu and Malang Diedhiou.