App.R

library(shiny)

my_df <- data.frame(values = c("A", "B", "C"))

ui <- fluidPage(
   div(id = "my_select"),
   tags$script(src = "select.js")
)

server <- function(session, input, output) {
  session$sendCustomMessage("my_data", my_df$values)
}

shinyApp(ui = ui, server = server)

select.js

/* I want to use the values from my_df */
Shiny.addCustomMessageHandler('my_data', function(color) {
  // the dataframe column is imported as an array
  console.log(color)
  my_array = Object.values(color)
  document.getElementById("my_select").innerHTML = 
  `<select>
  ${my_array.map(createOption).join("")}
  </select>`
});

function createOption(opt) {
  return `<option value=${opt}>${opt}</option>`
}

/*
But can I make this work:
Shiny.addCustomMessageHandler('my_data', function(color) {
  // the dataframe column is imported as an array
  console.log(color)
  my_array = Object.values(color)
});

 document.getElementById("my_select").innerHTML = 
  `<select>
  ${my_array.map(createOption).join("")}
  </select>`
*/