Bind IP to MAC addresses wthout DHCP

Is it possible to bind an IP address to a MAC without using DHCP?

yes, use static arp entries: http://www.mikrotik.com/docs/ros/2.8/ip/address.content#7.42.3

Yes, this is working well for me. Just set ARP mode on the interface connected to your clients to “reply-only” then enter MAC/IP combinations into the ARP table.