I have found the song. It is called "My Saviour is Calling," and it was written by Hylo Brown. It was first released on his 1962 Starday album, "Bluegrass Balladeer" (Click here) If you don't want to have to deal with that you can PM me and I'll send you the recording.

I was able to find it thanks to WFMU's online radio. It is around 12:05 into this playlist: https://wfmu.org/flashplayer.php?version=2&show=9157&archive=116031

The lyrics here are a combination of Brown's lyrics and the Alabama Bluegrass Boys' lyrics. Where they are the same they are normal. When there are brackets, it is how Hylo sang it, and the ones in parenthesis are how the Alabama Bluegrass Boys sang it.

MY SAVIOUR IS CALLING
Hylo Brown, 1962

Oh I have heard a voice a-callin'
Come up here and (know His name) [live with me]
Jesus is His callin' for His children
Calling under that land (where true and free) [where's love and free]

I can hear my Master callin'
As I walk along my way
I can see the gates a-glowin'
That I will live there some sweet day

Will you be ready, friends and loved ones
On that celberation* day
Don't turn your back on Christ the Savior
(Just) [Please] walk the straight and the narrow way

I can hear my Master callin'
As I walk along my way
I can see the gates a-glowin'
That I will live there some sweet day

We read in the Bible of John the Baptist
We also read of (Matthew and Luke) [Saint Matthew]
But if you'll trust in Christ the Savior
He'll give us a crown when we all get through

I can hear my Master callin'
As I walk along my way
I can see the gates a-glowin'
That I will live there some sweet day

*for some reason they both say "celberation" instead of celebration