SimonCa:
Hello both, thank you for your feedback.Can you suggest to me what can I do now to convert the AC output of the transformer into the DC output that I need? What piece can I add to the circuit?
Thank you very much.
No, that's not the way to go, you seem fixated on using an unsuitable component for the job.
Much simpler to power the Arduino from a suitable regulated DC power supply in the first place,
such as a good quality USB supply - you even have the right cable for this already...
Also I suggest getting a cheap multimeter with DC and AC voltage ranges before doing anything
else to avoid expensive errors like this. If a power source gives out any AC voltage its not a
regulated DC supply and not safe for the Arduino.