I use a connection string like this
library(odbc)
conexion <- dbConnect(odbc::odbc(),
.connection_string = "Driver={Microsoft Access Driver (*.mdb, *.accdb)};
Dbq=C:/path/to/your/access_file.accdb;",
encoding = "latin1") # This is only for data with non ASCII characters
Have in mind that the "Driver" parameter could be different depending on your Microsoft Access version (older versions use a different database engine)