Once you have your Rmd report ready, you can simply knit it to html and copy the file to the web server using FTP with something like this
library(rmarkdown)
library(RCurl)
render("path/to/your/rmd/file",
output_format = "html_document",
output_options = c("self_contained = TRUE"),
quiet = TRUE)
ftpUpload("path/to/the/rendered/html/file",
"ftp://user:password@server.ip//var/www/html/file_name.html")