It was made in 1927.
Is should be stamped with a code on the left side of the barrel in front of the receiver with the month and year. A diagram and code can be found on the Remington Society of America's website.
http://remingtonsociety.com/rsa/questions/barrelcodes
1920
I checked www.oldguns.net and they show the manufacture date of Remington 1903A3 serial no. 3851292 as 1942.
RW isn't part of the serial no, it stands for Remington Works 1915
That is not a serial no of a Remington 1911A1 they stopped in 1945 with 2465139.
It was made in 1927, it should also be marked on the left side of the barrel just in front of the receiver. You can get the Month/Year from that code and look up the location and chart on the Remington Society of America's website. http://remingtonsociety.com/rsa/questions/barrelcodes
1914
1913
1920
1919
late 1919
1920
1915