Who proposed the motion that gave Gaius Julius Caesar the title Augustus?

Octavian who would later become Gaius Julius Caesar Augustus:

My answer really focuses on the why as much as the who, because the reality may have been that in many ways he gave himself the title.

Octavian returned from Egypt with a wealth of treasure and a serious wealth of power. He was respected by his legions, of which he was commander of all sixty of them. Upon his return his fellow Romans believed they had seen the end of war and strife, and they hailed him as the Prince of Peace and benefactor of mankind. Octavian understood the importance of ensuring the people of Rome that he was benevolent. He certainly did not want to meet a similar demise to that of his great-uncle Gaius Julius Caesar (adopted father). So began a massive effort in religious renewal. Octavian restored 82 temples in one year alone. Also, there were grand new buildings like the Theatre of Apollo, and the Horologium. Octavian's right hand man Agrippa, too, embarked on several major building projects. Among these were the Pantheon, later rebuilt by Hadrian. Agrippa also repaired the city's water system and added two new aquaeducts, the Aqua Julia and the Aqua Virgo (Octavian famously quoted "I found rome of clay; I leave it to you of Marble") Rome was happy and Octavian had marble and possibly more importantly religion. Religion could be manipulated to suit the ambitions of Octavian and those he had given power to. Before we get to "those he had given power to" lets finish the topic of religion. Octavian recognized his prominence and equally recognized that without some shrewd decision making he had nowhere to go but down in regards to said prominence. His efforts to renew religious vigor throughout Rome would grant him a buffer during bad times and though one could assume that during good times he wouldn't receive the glory; they would be mostly wrong. Back to "those he had given power". The first form of "given" power would be the priesthood. Restoring temples meant restoring priests, of which Octavian had both subtle and secure power over. The second form and most noticeable to those with nobility was the purge and restoration of the senate. In 27 BC Octavian is famous for transferring power back to the Senate, but what really happened? The following two snippets do a great job of explaining this.

Why was Augustus so successful in creating the Roman Empire?

...

The fact of the matter was: the main body of the senate owed their careers to Augustus, and there was nothing that could be done about it – as Tacitus would want us to believe, Augustus’ grip on the senate was too strong. For instance, when Octavian returned to Rome after the civil wars had been extinguished, his censorial powers made it possible for him to purge the Senate of any potential resistance in his regime. The reason for such a rash act was due to the number of senators appointed by Octavian’s rival triumvir; the presence of senators that did not side with him during the Actium campaigns was also an adequate reason for an assessment. Thus in 29 BC, Octavian removed 190 potential threats to his administration ...

Why was Augustus so successful in creating the Roman Empire?
(www.unrv.com)

Octavian becomes Augustus Caesar

...

In 27 BCE, Octavian began his seventh term as consul. He renounced his consulship and declared that he was surrendering all powers to the Senate and other bodies, including control of the army. It was a bogus withdrawal from power. As Octavian expected, the Senate, packed with his supporters, responded by returning much of his power, claiming that it was doing so for the sake of unity and relief from factionalism and civil strife.

...

In keeping with his great prestige,the Senate gave him a title that had the ring of his being divinely chosen: Augustus Caesar. And the Senate made it law that he be included in the prayers of Rome's priests. In appearance, the republic had been restored, but in fact ultimate power still lay with Octavian -- Augustus Caesar. ...

The ROMAN REPUBLIC'S CIVIL WARS and FALL (7 of 7)
Octavian becomes Augustus Caesar (www.fsmitha.com)

So in 29 BC two years prior to his "benevolent" action of giving up the power he ensured that he indeed would not really be giving up anything, well at least not in terms of power (He "had" religion and he had the Senate). It should also be noted that 29 BC was not the only time he reduced the number of Senators.

If you absolutely had to break this down into one person other than Octavian himself who would have been responsible for the title of Augustus being handed out, I would suggest that person was Marcus Vipsanius Agrippa. Agrippa was "his right hand man" but possibly even more important he was Octavian's highest military aid, closest consul, son in law, and soon after their return to Rome, a member of the Senate. That being said, Agrippa was just one of about 800 members in the senate at that time.