I read that semetic languages were introduced to horn of africa around 800BC. Was there any major migration southward from the Crescent region around this time?

In Foundations of an African Civilization, Aksum and the Northern Horn 1000 BC-AD 1300, David Phillipson says the following on pp 11:

Languages of the Semitic family – which also includes Arabic and Hebrew – are today spoken over wide areas of northern Africa and western Asia. Those of the northern Horn form a distinct Ethio-Semitic linguistic group comprising principally Tigrinya, Tigré and Amharic, together with a number of more southerly languages and the older form – Ge‘ez – that survives in liturgical use by the Ethiopian and Eritrean Orthodox Churches. The Ethio-Semitic languages – with others that have been spoken in Arabia – are classified as South Semitic.

....

The most widely accepted interpretation of these observations has been that South-Semitic-speakers established themselves in territory that had previously been occupied by a Cushitic-speaking population. The former belief that this arrival of South-Semitic-speakers took place in about the second quarter of the first millennium BC can no longer be accepted in view of linguistic indications that these languages were spoken in the northern Horn at a much earlier date.8

And he cites the following papers:

G. Hudson 1977. Language classification and the Semitic prehistory of Ethiopia. Folia Orientalia 18: 119–66.
G. Hudson 2000. Ethiopian Semitic overview. Journal of Ethiopian Studies 33, 2: 75–86
D. Appleyard 1978. Linguistic evidence of non-Semitic influence in the history of Ethiopian Semitic: lexical borrowing in Ge‘ez and other Ethiopian Semitic languages. Abbay 9: 49–56.
R. J. Hayward 2003. Entry under ‘Cushitic’. in S. Uhlig (ed.) 2003a. Encyclopaedia Aethiopica, vol. 1. Wiesbaden: Harrassowitz.: pp 832–9.

So, if we take Phillipson at his word, South Semitic languages would have been spoken in what is now Eritrea and the Ethiopian highlands long before 800 BC. Though, in Chapter 3 of Foundations of an African Civilization Phillipson also says that inscriptions of South Semitic languages first date to the first millenium bc. So, it might be correct to say that our first evidence of those languages come from writings circa 800-600 BC, and linguists and archaeologists are left to puzzle how long unattested spoken language was in the region before then.

Now, I have to mention an important point. Your question asks "Was there any migration from the Crescent region around this time?"

Languages like Akkadian or Aramaic are classified as North Semitic languages, whereas languages like Sabaean (from Yemen), Ge'ez, Tigre and Amharic are classified as Southern Semitic.

So, no. There is not evidence of migration from the Fertile Crsecent region introducing semitic language to the Horn. If that were the case, proto-Ge'ez inscriptions would have syntax more like Aramaic or Akkadian. But the syntax of inscriptions, and living spoken languages, resemble Sabaean much more closely.

The most parsimonious explanation is that Southern Semitic languages crossed the Gulf of Aden from Yemen to what is now Eritrea, and then spread into the highlands.

If you want to read more about this, Chris Ehret covers it in History and the Testimony of Language which is a Linguistic history textbook.