Try the following with RODBC:
odbcDriverConnect(connection = "Driver=FreeTDS;TDS_Version=7.2;Server=mydns.database.windows.net;Port=1433;Database=mydatabase;Uid=myuserid;Pwd=mypass;Encrypt=yes;TrustServerCertificate=no;Connection Timeout=30;")
You will need to allow access from the following IP addresses:
- 54.204.34.9
- 54.204.36.75
- 54.204.37.78