Probably the best way is to use dplyr. I recreated your data below and used the mutate function to create a new column on the dataframe.
#Creation of data
Client <- c("RP","DM")
Score <- c(125,30)
DF <- data.frame(Client,Score)
DF
#install.packages("dplyr") #Remove first # and install if library doesn't load
library(dplyr) #If this doesn't run, install library using code above.
#Shows new column
DF %>%
mutate("%" = round((Score/sum(Score))*100,1))
#Overwrites dataframe with new column added
DF %>%
mutate("%" = round((Score/sum(Score))*100,1)) -> DF
Using base R functions the same goal can be achieved.
X <- round((DF$Score/sum(DF$Score))*100,1) #Creation of percentage
DF$"%" <- X #Storage of X as % to dataframe
DF #Check to see it exists