You can connect only the the line with which the ESP-01 transmits to the Arduino's receiver, and accomplish one-way data transfer.
However, the ESP will have to be willing to transmit without prompting, and you will not be able to use the Arduino to setup or configure it. Further, you will not be able to use any in-band signalling to ask the ESP to refrain from sending, so you will have to be sure that your Arduino sketch is generally ready to claim any input which may arrive, and that if there are periods when it is not, the behind-the-scenes serial buffer is large enough.
There's also the question if it is safe to connect the ESP transmit pin directly to the Arduino receive. In the intended direction of operation, it is. But should you ever load code on the Arduino which uses that pin as a GPIO output, there is some risk of damage to the ESP. It's up to you to decide if careful usage will be enough to prevent that; if not, you may want to try something like a 1K series resistor and a schottky diode to clamp the line to the ESP's 3.3v supply, in a way that diverts the current from any accidental 5v output around any internal protection diode that may have more limited power handling.