The 29-year-old was given a hostile reception last weekend by the Juve faithful, who unveiled a banner describing the striker, who had previously turned down the opportunity of a permanent move to Turin, as a "mercenary".
"I have great respect for Juve fans and I will do all I can to earn their trust," he said. "I am aware that I have joined a group where there is a lot of competition for places.
"But the important thing is that all of us give our all for the good of Juventus.
"No one has promised me anything but I want to do well and earn a regular place in the team.
"I want to be an additional weapon for this club even though the coach will have the final say as to who plays."
Borriello has another motivation to do well with the Turin giants as Juve have an option to make his move permanent in the summer.
"I also want to convince the Juve executives to acquire my rights at the end of the season," he said.
Unbeaten Juve know they could take over sole possession of first place if they beat Cagliari and AC Milan fail to take all three points against Inter this weekend.
The Bianconeri are level on 37 points with Serie A leaders Milan.
Cagliari have won just two of their 31 league encounters at Juventus over the years, but coach Davide Ballardini is optimistic the team can build on last weekend's 3-0 win over Genoa.
That result ended a three-game winless run for Cagliari and lifted them to 10th in the standings.
"This result was a big boost in confidence in view of our game at Juventus," Ballardini said. "We had failed to score in our previous three games and my players were hungry to get a result and produce a solid display in front of our home fans.
"Now we need to show the same attitude in Turin, knowing we face a very tough opponent."
Juve will be without suspended defender Giorgio Chiellini and injured striker Fabio Quagliarella this weekend.