This can be a way:
$ awk 'NR==FNR {a[$2]=$1; next} $1=a[$1]' file2 file1
rs11805559
rs728917
rs728918
rs11264495
rs1609666
rs1171564
rs6427315
Explanation
Firstly it loops through the second file and stores the array a[number]=rxxxx
. Then it loops through the first file and replaces the field with its value in the array.