According to the council's website parents should have received their offer letter as an email attachment.
They say: "You will be sent an email, with your offer letter attached, on April 16, 2019."
However instead parents have received a link to an online portal that is not letting them log in.
This has caused frustration and anger amongst parents with hundreds of comments on the council's social media which state people are unable to find out which school their child has been offered a place at.
On Twitter, Leanne Mann said: "Hundreds, possibly thousands, of anxious parents are not able to log into the portal for primary school places after Leeds council changed the process of finding out which school you have been accepted to."
Many nervous parents have been trying to log on since the early hours of Tuesday, April 16.
Charlotte Francis said: "Come on Leeds city council.
"I have been trying to access the website since 2.15am this morning.
"You have provided incorrect information as to how we would be informed on your website.
"Parents across Leeds are angry and frustrated!
"This is so important to so many people and totally unacceptable."
Leeds Council Help tweeted: "We are aware that some parents are struggling to access the online portal to check primary school places.
"Please be patient whilst we investigate this, we appreciate that you want to know your offer information as soon possible and we are working on resolving this ASAP."
Leeds council confirmed the portal was working again shortly after 9am.
They tweeted: "We can confirm the online portal is now back up and running and parents can now log in to check their primary school offers. Apologies for any inconvenience caused."