Here is the full text by Anne Steele, which includes a second verse omitted in the arrangement above:
1 Dear refuge of my weary soul,
On thee when sorrows rise;
On thee, when waves of trouble roll,
My fainting hope relies.
2 While hope revives, though pressed with fears,
And I can say, "My God,"
Beneath thy feet I spread my cares,
And pour my woes abroad.
3 To thee I tell each rising grief,
For thou alone canst heal;
Thy word can bring a sweet relief,
For every pain I feel.
4 But oh! when gloomy doubts prevail
I fear to call thee mine;
The springs of comfort seem to fail
And all my hopes decline.
5 Yet gracious God, where shall I flee?
Thou art my only trust;
And still my soul would cleave to thee,
Though prostrate in the dust.
6 Hast thou not bid me seek thy face?
And shall I seek in vain?
And can the ear of sovereign grace
Be deaf when I complain?
7 No, still the ear of sovereign grace
Attends the mourner's prayer;
O may I ever find access,
To breathe my sorrows there.
8 Thy mercy-seat is open still;
Here let my soul retreat,
With humble hope attend thy will,
And wait beneath thy feet.
The Christian's duty, exhibited in a series of hymns, 1791
The sheet music is available to print at no cost here:
http://s3.amazonaws.com/ruf-hymnbook-prod/hymns/431/original/dear-refuge-of-my-weary-soul.pdf?1355798948 .