To establish a connection with a Kafka server in Rust, you can use the 'rDKafka' library which provides bindings for the librdkafka C library. First, you need to include the 'rDKafka' library in your Rust project's dependencies. Then, you can create a new producer or consumer instance by configuring the necessary settings such as brokers, topic, and group ID. After configuring the instances, you can start sending or receiving messages to/from the Kafka server.