For a $25 donation, the ads will be shown to 1800 people on "websites internet users see everyday", while a $100 donation will mean they are seen by 10,000 people, the group said.
"How broadly and how long we can run the ads for depends on how much money we can raise," said GetUp! national director Simon Sheikh.
"That's why we're calling on all Australians who disagree with (Communications Minister Stephen) Conroy's censorship plans to chip in."
Since being launched this afternoon, the drive has already raised more than $10,000.
Meanwhile, thousands of users on social networking website Facebook have flagged their intention to attend protests against the filtering plan in cities across the country.
The protests, to be held on December 13, have been organised by the Digital Liberty Coalition, a collection of anti-censorship groups including GetUp! and the Electronic Freedom Project.
Opponents of the Government's filtering scheme are concerned the system will slow internet speed and accidentally block a large number of legitimate websites.
In the first of three annual reports made for Senator Conroy's office published earlier this year, the Australian Communications and Media Authority cited studies that had found web filters blocked the wrong content in more than 25 per cent of test cases.
Anti-censorship advocates are also concerned that a secret "blacklist" of websites to be blocked could be expanded in the future to include political material.
The Government says an internet filter is necessary to clamp down on illegal material such as child pornography and protect young people on the web, but has struggled to convince all parties.
Last month it was reported that even some children's welfare groups were opposed to the plan, with concerns that money put aside for a web filter could be better spent elsewhere.
"This is called a child protection measure yet the vast majority of all serious child abuse does not occur on the internet, it occurs in the home," said James McDougall of the National Children's and Youth Law Centre.
A live trial of web filtering technology to censor a blacklist of up to 10,000 websites is scheduled to begin before Christmas.
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Ryan of Contral Coast