In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is recommended for the person who is praying alone to say the adhan and iqamah.
Answering your question, the Fatwa Center at Islam Q and A, states:
It is recommended for the person who is praying alone to say the adhan and iqamah because of the general meaning of the reports that refer to them.
Sheikh Mansur Al-Bahwati (may Allah have mercy on him) said:
“They (the adhan and iqamah) are Sunnah (for the person who is praying alone) because of the general meaning of the hadith of Uqbah ibn Amir, who said that the Prophet (peace be upon him) said: “Your Lord likes it when a shepherd at the top of a mountain pass calls the adhan for prayer and then prays. Then Allah says, ‘Look at this slave of mine, saying the adhan and the iqamah for prayer and fearing Me. I ask you to bear witness that I have forgiven My slave and will admit him to Paradise.’” (An-Nasa’i)
The adhan and iqamah are also Sunnah for travelers, because the Prophet (peace be upon him) said to Malik ibn al-Huwayrith and his cousin: “When you two travel, say the adhan and iqamah for prayer, and let the elder of you lead the prayer.” (Agreed upon, see Matalib Uli an-Nuha)
It is disliked for him to neglect the adhan and iqamah. Al-Shafa’i (may Allah have mercy on him) said:
“If a man neglects to say the adhan and iqamah when he is praying alone or in congregation, I regard that as disliked, but he does not have to repeat the prayers he did without the adhan or iqamah.” (Al-Umm)
Almighty Allah knows best.