It’s hard for me to guess how to pronounce words beginning with re- correctly.
Sometimes it is /rɛ/ as in reference, but sometimes it is /ri/ as in report.
Is there any rule about this?
Rule: Use a Dictionary
Yes, there is a rule, and that rule is that you must look them up in a dictionary if you are not a native speaker.
That’s because words beginning with re- in English can, depending on the word, be pronounced with any of eight different vowels:
The last three or four at the end of that list tend to be for native words, while the ones at the beginning tend to be for unassimilated imports.
But in diphthongs like reindeer or reynard — let alone reiter or rearward — all bets are off.
Here’s an alphabetized sample list, with pronunciation following:
And here grouped by pronunciation:
Tchrist's answer does a good job of showing the variance in pronunciation for words starting with "re." However, there are some patterns, so I thought I'd make a post describing them, since some people might find it useful information. In particular, the pronunciation is a lot more predictable if we only look at words with the prefix re- (derived from Latin, with the general meaning of "again") rather than all words that happen to start with the letters "re" (like "reindeer" and "reiter"), and if we exclude recent borrowings from other languages like rendezvous and redondilla.
John Wells's phonetic blog has a good post that describes the usual pattern. I've copied the main bit of it below for ease of reference; keep in mind that he uses e to represent the vowel in the word dress (it means the same thing as the symbol ɛ used in tchrist's post):