The striker will make his competitive debut for Ayr United on Sunday when Ally McCoist's side make the short trip to Somerset Park.
The 32-year-old endured an injury-hit spell at Ibrox last term before leaving the Gers by mutual consent in March after only a handful of appearances.
Kyle told SportTimes: "I don't have a point to prove at all. It was unfortunate how things worked out at Rangers.
"I got injured just before Christmas and I didn't get back in time for one reason or another.
"I had a trial for two weeks at Rangers to try and win a deal there last year and Ally offered me a contract so I have got nothing to prove.
"When I was given a chance, I did well and scored goals.
"I was gutted that I got injured and that it ended the way it did for me at the club.
"I am pleased that Rangers have started the season so well.
"They have got rid of the cobwebs from last campaign and they are doing what they should be doing at this level and winning games comfortably and putting on a show for the fans.
"I am pleased for them, pleased for the manager and pleased for my former team-mates that they are getting it right and heading in the right direction."
Rangers have started the campaign in stunning form as McCoist's men have raced clear at the top of the SPFL League One standings with seven successive wins.
The Light Blues line-up is considerably different from the side which Kyle featured in last season following the arrival of nine new signings during the summer.
And the former Kilmarnock and Hearts target man is delighted to see friend and former team-mate Lee Wallace, who has been called up to Gordon Strachan's Scotland squad, playing an integral part of the Gers' success this season.
Kyle said: "I was with Lee at Hearts and, for me, he is the best left-back in Scottish football.
"Of everyone who is available to play left-back for Scotland, Lee is head and shoulders above the rest of them.
"He will help Rangers get to the Premiership and I am sure when he does he will be the Scotland left-back.
"I am surprised that nobody has come in and taken a gamble on him already. To be honest I think he is more than capable of playing in the Barclays Premier League.
"Mick McCarthy phoned me a few years ago about him and he was keen to get a hold of him.
"He has stuck by Rangers through thick and thin and he is being rewarded now.
"The fans have taken to him, they appreciate everything he has done for the club and the class he shows."