The Washington Post fact checked this claim and scored in 2 (of 4) Pinocchios.
While it's true that the number of Syrian Christian refugees admitted to the US is disproportionately lower, it's not clear why.
The WP article lists the number of Syrian refugee for 2016 by religion as:
Muslim Sunni: 15,134
Muslim Shiite: 29
and notes that the number of Christians comes from adding up the different denominations (catholic, protestant, baptist, etc). (I came up with 32 more Christians - it seems the WP forgot to add in people who reported they are Orthodox.)
The article reports that when asked about Christian refugees, António Guterres, then U.N. High Commissioner for Refugees, indicated that he believes that most Syrian Christians have gone to Lebanon due to the relative large Christian population there and long standing ties between the two countries.
Others have taken his comments to mean that the UN is not willing to let Christians leave the Middle East region.Since most refugees register with the UN before applying for asylum in the US, it's possible that some are steered away.
All of this of course is highly speculative, US law allows asylum on the bases of religious persecution, but there is nothing specific that applies only to Christians and not Muslim.
This is illustrated by this chart published by Pew:
While a record number of Muslim Refugees were admitted in 2016 compared to previous years, it was still about equal to the number of Christians.
So in conclusion: The number of Syrian Christian refugees is lower than expected, but the number of Christian refugee overall is not. That indicates that being a Christian is not a significant negative factor when applying for asylum.
The complete pew article can be found here.