The Syrian Democratic Forces (SDF) said the move had opened up a second front inside the Syrian city. They entered the eastern part earlier this week.
Its fighters were engaged in fierce clashes with the jihadists, it said.
The SDF, supported by US-led coalition air strikes, has spent months encircling the city.
"The SDF captured the western half of the Al-Sabahiya neighbourhood and are reinforcing their positions there," the head of the Syrian Observatory for Human Rights monitoring group, Rami Abdel Rahman, told AFP news agency on Saturday.
"They then advanced north to the adjacent district of Al-Romaniya and are fighting IS there."
A statement from the SDF's Operation Wrath of the Euphrates said its fighters had stormed Al-Romaniya and were locked "in fierce fighting inside the district".
Raqqa, which has been held by IS since 2014, is an important hub for the jihadist group's operations and is reportedly defended by up to 4,000 fighters.
Tens of thousands have left the city as fighting intensifies.
The SDF is an Arab-Kurdish alliance that was formed in 2015.
As well as holding part of Al-Sabahiya in the west, the alliance also controls Al-Meshleb in the east. But it has struggled to advance from the city's north, which is heavily defended.
"IS has reinforced the northern approach to Raqqa much more, thinking that's how the SDF would try to advance on the city," Mr Abdel Rahman said.
"The western and eastern entrances to the city were much less fortified."