There is no Web API, but you can perform this using SQL.
You can do it simply with "Presto Ethereum Connector" (https://github.com/xiaoyao1991/presto-ethereum)
Using Presto Ethereum, you can query the blocks using an SQL command. You can base the where condition on block_timestamp.
Bellow is the structure of the "block" table provided by Presto Ethereum:
DESCRIBE block;
Column | Type | Extra | Comment
-----------------------------------------------------------
block_number | bigint | |
block_hash | varchar(66) | |
block_parenthash | varchar(66) | |
block_nonce | varchar(18) | |
block_sha3uncles | varchar(66) | |
block_logsbloom | varchar(514) | |
block_transactionsroot | varchar(66) | |
block_stateroot | varchar(66) | |
block_miner | varchar(42) | |
block_difficulty | bigint | |
block_totaldifficulty | bigint | |
block_size | integer | |
block_extradata | varchar | |
block_gaslimit | double | |
block_gasused | double | |
block_timestamp | bigint | |
block_transactions | array(varchar(66)) | |
block_uncles | array(varchar(66)) | |