Not being a native English speaker, I feel that there is some difference in meaning between
Call to action
Call for action
However my research was unfruitful. Is there a difference between these two expressions?
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Putting aside the different grammatical constraints mentioned by @Gaston Ümlaut, there are constructions where either preposition can be used but the meaning usually differs...
...where in most cases a "call to action" is addressed to either the population at large, or everyone within some substantial community, but a "call for action" is normally addressed to government, or the leaders of some organisation (note that "a call to arms", which is far more common than either of these, is also invariably addressed to large numbers of people, not to leaders).
In most cases, a "call to action" actually seeks to persuade large numbers of people to do something "intermediate", which will put pressure on leaders to carry out the desired "action" (everyone should write to their government representative, so the government will change some policy, for example). It's fairly unusual to see the expression "call to action" used in contexts where people at large are being asked to do something that directly resolves some problem (turning down house thermostats to combat global warming, for example).
Effectively, a "call to action" asks everyone to agree action should be taken, but a "call for action" asks the relevant people to actually do it.
This is an example of how a verb's semantics change with different prepositional complements. I think the difference in meaning can be seen by considering some different forms of the verb such as:
It seems to me that 2 is probably ungrammatical and needs an object, such as:
Based on this, the phrase 'call for action' appears to be focused on the need for action, whereas 'call to action' is focused on the need for someone (who the hearer may be able to identify) to act.
(Disclaimer: Just a quick analysis, I'm sure it could be improved substantially by someone who's researched this issue)