Cambridge Assessment, which owns OCR, hopes for "millions of questions", with the best appearing on exam papers in England within the next five years.
OCR would check all questions to see they are of the right standard.
But there are concerns these "crowdsourced" exam questions could give some pupils an unfair advantage.
Cambridge Assessment research director Tim Oates told the TES: "Really interesting questions which - put to children - encourage them to think hard, to integrate things, to understand things and challenge their ideas a bit, are really important.
"We don't think we should necessarily just commission those through asking a limited number of people.
"We want to know what questions teachers ask in the classroom and whether they were good for unlocking that bit of thinking or revealed that misconception."
Currently, exam papers are drawn up by exam committees made up of teachers with detailed knowledge of each subject.
Plans are at an early stage of development and would need to be approved by the exams regulator Ofqual in order to go ahead.
However, Mr Oates said: "I can see within three to five years' time we might be able to start doing some work [with crowdsourced questions] in formal examinations."
OCR said questions would have to go through technical and tough quality assurance processes before being used in a real exam.
The questions submitted by teachers would also be made available to other teachers online through a question bank, so that they could be used in the classroom.
School leaders and assessment experts have welcomed the idea of an online question bank for teachers.
Malcolm Trobe, interim general secretary of the Association of School and College Leaders, said: "The only potential weakness I can see in the system is, if I'm sending in questions and using the same questions in preparation for the examination, if they then turn up on the exam paper it advantages those youngsters because they're seeing a question they're familiar with.
"You're going to have to find a way of overcoming that."
But Mr Oates said schools already guessed exam questions and prepared pupils for likely questions using past papers.
He said the "crowdsourcing" approach would not create unfairness because there would be so many questions in the pool that teachers would have little incentive to drill pupils for any particular question.
OCR and Cambridge Assessment are already working on a project to crowdsource questions from computing teachers, which will be available to other teachers to use in classroom-based assessments.

State-owned Chinese insurer PICC Property and Casualty Company is buying the shares.
Deutsche announced earlier this year it would sell the stake as part of a plan to bolster its finances.
"As we execute on Deutsche Bank's strategic agenda, now is the right time for us to sell this investment," said chief executive John Cryan.
In October, the bank said it would be cutting 15,000 jobs and selling various businesses as it looked to stem losses.
Deutsche posted a â‚¬6bn (Â£4.4bn) loss for the third quarter.

The Swede, 35, joined Jose Mourinho's side last summer on a one-year deal and has scored 20 goals this season.
Mourinho said on Friday he believed the club's top scorer would still be at Old Trafford in 2017-18.
When asked about his future, Ibrahimovic said: "We'll wait and see."
Ibrahimovic's goals have helped Manchester United into the EFL Cup final - where they will face Southampton - as well as the fifth round of the FA Cup. The Red Devils are also in the Europa League knockout stage.
Manchester United won the Community Shield in August and Ibrahimovic is confident of adding at least one more trophy to the collection.
"We have one and we can get our second one," he added.
"We are still in the Europa League and FA Cup, so if we don't become champions in the Premier League at least we can try and win two or three trophies."

Malcolm Wright, 56, was taken to Aberdeen Royal Infirmary with serious injuries following the incident in the Peter Buchan Drive area last month. He died later.
Gary Crossan, 30, of Peterhead, appeared at the town's sheriff court charged with murder.
He made no plea and was remanded in custody.
Teachers are to be asked to submit challenging GCSE and A-level exam questions by a key exam board, the Times Educational Supplement reports.
[NEXT_CONCEPT]
Deutsche Bank has agreed a deal to sell its 20% stake in China's Hua Xia Bank for up to 25.7bn yuan ($4bn).
[NEXT_CONCEPT]
Manchester United striker Zlatan Ibrahimovic says "nothing is done" with regards to his future but insists he has fulfilled requirements needed to extend his contract.
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A man has appeared in court charged with murder in Peterhead.