Altering the existing partition which is partitioned by date range in SQL Server 2012
Yes, but I wouldn't recommend it. Splitting partitions with lots of data takes an unpredictable amount of time and typically eats a ton of transaction log. I'd insert the data into a new table with the correct partitioning. It's more work, but you are in control of the move. Best practice (hindsight's 20/20) is to always have an empty left and right partition for these types of scenarios.

Best Practices

Always keep empty partitions at both ends of the partition range to guarantee that the partition split (before loading new data) and partition merge (after unloading old data) do not incur any data movement. Avoid splitting or merging populated partitions. This can be extremely inefficient, as this may cause as much as four times more log generation, and may also cause severe locking.

https://msdn.microsoft.com/en-us/library/ms186307.aspx