You can do this by setting alpha in the geom_smooth() geom. See reprex, below:
library(ggplot2)
ggplot(mpg, aes(displ, hwy)) +
geom_point() +
geom_smooth()
#> `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggplot(mpg, aes(displ, hwy)) +
geom_point() +
geom_smooth(alpha = 0.3)
#> `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggplot(mpg, aes(displ, hwy)) +
geom_point() +
geom_smooth(alpha = 0.1)
#> `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Created on 2018-12-12 by the reprex package (v0.2.1.9000)
See also this answer on StackOverflow for how to control the opacity of the line and the ribbon separately: