4-5 Weeks for an Actual Citizen Farmer
The actual time it will take news to reach Anatolia is 2-6 weeks depending on exactly where the farm is. Since this is a "citizen" farmer, this means he is probably somewhere near the Roman Colonia Şebinkarahisar which is 4 weeks away from Rome and the only place in Anatolia where you might have found citizen farmers at this time. So, while news of Caesar's Death may first reach the region in just a 2 weeks, a citizen farmer would live no less than 4 weeks from Rome.
As for a minimum time-frame: a citizen farmer would probably learn of the event much sooner than most other farmers would. Just before his assassination, Julius Caesar was planning to pass through this region to wage war on Parthia. This would have been a very significant event for the farmer who would have been expected to either supply the army as it passes through or be drafted into it. Being a citizen, he was likely already preparing for the later by the time Caesar was killed; so, news of his death would have been especially important news to this particular farmer at this particular time and place. So much so, that it is likely the local legate would have to dispatch new orders to the citizen farmer to compensate for news of Caesar's death.
2-14 Weeks for a Non-citizen Farmer
While the death of the Emperor is certainly gossip worthy, it's not vital news to the common farmer. This means that it is unlikely for someone to hear news of Caesar's death and bee-line it out into the countryside to let this random guy know about it.
The most likely time for a rural farmer to learn about it will be when he is going into town to sell his wares since this itself would be the event where news like this would normally be learned by a rural farmer. Julius Caesar was assassinated on March 15th; so, to know when the farmer would be going into town next, we need to know what crop he was growing. The most common spring/summer crop of Mediterranean Farmers was wheat. Wheat's harvest season in Anatolia lasts from April to Late May. But before he can deliver his harvest, he first needs to dry and thresh it. Due to the laborious nature of Roman Threshing techniques, we can assume this will take another 3-4 weeks meaning that a typical time for an Anatolian Wheat Farmer to arrive in town with his harvest would be some time in Late June or Early July.
While it is always possible that news could arrive at this particular farm at any point after the news arrives in town, news will generally travel much slower between April and Late June because of the time sensitive nature of harvest season. So, while 2 weeks is possible, 14 weeks is more probable.