Is it safe to use file's hash as IV? I'm encrypting some files using AES in CBC mode.  

I'm also using file's digest (SHA-1) to check that data is decrypted correctly (so I need to store it with file).

Is it safe to use this digest as AES's IV and store it in the header of file? Or it has security issue?
By using the file's hash as IV, you also divulge the file's hash. This allows an attacker to make an exhaustive search on the file contents. It is not difficult to imagine situations where there are only a few millions or billions of possible file contents (e.g. the file contents are an encrypted SAN or password), in which case showing the data hash is an intolerable leak.

What you could use as IV is the result of HMAC over the file, using as key the same key than for encryption (or, preferably, derive both the HMAC key and the encryption key with a suitable PRF). The result would probably be quite hard to prove secure in any way, so don't do it for production; but it seems like a promising way to achieve context-free deterministic encryption.

"Context-free" means "without any memory". Some encryption modes require a random, unpredictable IV, while others just need nonces (e.g. a counter); you can obtain the former from the latter by encrypting the nonces with a block cipher, using a specific secret key for that. A counter still requires a bit of memory, which, depending on the situation, may or may not be easy to obtain. Some embedded systems would have difficulty updating a stored counter (permanent storage update draws a bit of current, a scarce resource on passive RFID systems). Since embedded systems rarely own a reliable source of randomness, they need deterministic encryption. Context-free deterministic encryption is thus an important niche functionality. Using HMAC to compute the IV for encryption may be a way to achieve that (with the important drawback of requiring a first pass on the whole file, before obtaining the IV which is need to begin encrypting it).