Yes, every transaction must pay a small fee to send transactions to the DAG. The amount of Bytes in transaction fee is determined by the size of your transaction. For example, if your transaction's data consumes 800 bytes of disk space, the fee to submit that transaction to the DAG will be 800 Bytes of the currency. This allows for low, predictable fees.
A typical payment transaction takes about 800 bytes, which is about $0.00001 at the current rate.